This document presents a theoretical model for predicting Lamb wave dispersion and attenuation in composite materials. The model accounts for anisotropic wave attenuation in composites by using a complex stiffness matrix for each unidirectional ply. Experimental validation was performed by measuring the complex stiffness of a CFRP laminate using laser interferometry and comparing predicted and measured group velocities and attenuations. The model was implemented in a software called FIBREWAVE that can predict Lamb wave behavior for composites with arbitrary layups given the complex stiffness matrix of the plies.
This summary provides the key points in 3 sentences:
The document discusses polarization errors in fiber optic gyroscopes that use fiber ring interferometers. It shows that applying polarizing fibers at the input and in the sensing coil can significantly suppress polarization errors. Using polarizing fibers at both locations can radically reduce errors by suppressing interfering polarization modes before they propagate through the sensing coil.
This document analyzes the polarization and transmission effects of antireflection coatings for silicon-on-insulator (SOI) material systems using simulation software. Without a coating, transmission of transverse magnetic (TM) polarized light is slightly higher than transverse electric (TE) polarized light. A single-layer antireflection coating is designed and optimized to increase average transmission by 19%, reducing the polarization effect. However, multilayer coatings did not further increase transmission over the optimized single layer. In conclusion, antireflection coatings can effectively reduce polarization dependence for SOI materials while improving overall light transmission.
Comparative theoretical study of polarising panda type and microstructured fi...Kurbatov Roman
This document summarizes a comparative study of different types of polarizing fibres for use in fibre-optic gyroscopes (FOGs). It compares Panda-type fibres with W-index profiles and depressed cladding, as well as microstructured fibres. It analyzes the spectral width of their single-polarization windows while considering bending, and their splice losses when spliced to conventional fibres. A new type of match-clad Panda fibre that polarizes without bending is also proposed. Simulation methods are described for modeling the mechanical stresses and optical properties of the different fibre designs.
New optical w fiber panda for fiber optic gyroscope sensitive coilKurbatov Roman
This document proposes a new type of optical fiber called a W-fiber Panda that could improve fiber optic gyroscopes. The fiber has a core with nitrogen doping surrounded by stress-applying rods that create birefringence. Testing showed a polarizing version had 3 dB/km x-mode losses and 30 dB/km dichroism, while a polarization-maintaining version had ultra-low losses of 0.35 dB/km. This new fiber combines advantages of existing fibers by allowing a wide single-polarization spectral window as well as a desired mode field diameter. Its low losses could enable longer or more sensitive fiber optic gyroscope coils.
Optimization of Aberrated Coherent Optical SystemsIOSR Journals
This document summarizes research on optimizing the image quality of aberrated coherent optical systems through apodization. It studies how apodization filters can be used to reduce edge effects like ringing, gradient, and shifting caused by aberrations like defocus, coma, and spherical aberration. The results show that at certain apodization parameter values and aberration combinations, the image quality is improved with minimum edge shifting and improved edge gradient. Specifically, an apodization parameter of 0.75 eliminated edge ringing for various aberration combinations studied. Thus, apodization can help mitigate the degrading effects of one aberration through the introduction of other aberrations.
1) Using four laser beams, researchers generated a three-dimensional optical lattice that traps 490nm polystyrene spheres in solution, forming a face-centered orthorhombic crystal structure.
2) The four-beam setup produces a stable periodic potential in all three dimensions that counteracts particle diffusion via radiation pressure balance.
3) Calculations show the four-beam lattice with all beams polarized parallel produces a simple intensity pattern that yields a face-centered orthorhombic crystal structure when the beam angle is 45 degrees.
Fiber polarizer based on w lightguide pandaKurbatov Roman
This document summarizes the optical properties of three types of fiber polarizers based on panda-type W lightguides with different lengths: 200 m, 1 m, and 50 mm. For the 200 m and 1 m lightguides, dichroism (polarization dependent loss) is higher than 30 dB due to a difference in cutoff thresholds between the fundamental x and y modes. For the 50 mm lightguide, an additional scattering layer is included near the cladding boundary to achieve dichroism higher than 15 dB. The physical mechanisms behind the dichroism in each case are also described, including the effects of microbending and macrobending losses.
Theoretical study of metal clad optical waveguide polarizerijsrd.com
In this paper, the metal clad optical waveguide polarizer have been analysed and presented. The metal's that were used are Gallium Arsenide and Aluminium for the cladding purpose of comparison and analysis. It was found that the variation between TE mode and TM mode when Gallium Arsenide is used as the cladding is less as compared to Aluminium. This is due to the metal cladding itself will cause a cut-off region in the polarizer. Gallium arsenide may have fewer modes compared to aluminium and which resulted in the variation of the graphs between the two metals used. We have also shown that there is a slight drop of the TM to TE loss ratio when the buffer layer thickness is increased. It was also found that the high extinction ratio results in the high and linear attenuation in the fiber.
This summary provides the key points in 3 sentences:
The document discusses polarization errors in fiber optic gyroscopes that use fiber ring interferometers. It shows that applying polarizing fibers at the input and in the sensing coil can significantly suppress polarization errors. Using polarizing fibers at both locations can radically reduce errors by suppressing interfering polarization modes before they propagate through the sensing coil.
This document analyzes the polarization and transmission effects of antireflection coatings for silicon-on-insulator (SOI) material systems using simulation software. Without a coating, transmission of transverse magnetic (TM) polarized light is slightly higher than transverse electric (TE) polarized light. A single-layer antireflection coating is designed and optimized to increase average transmission by 19%, reducing the polarization effect. However, multilayer coatings did not further increase transmission over the optimized single layer. In conclusion, antireflection coatings can effectively reduce polarization dependence for SOI materials while improving overall light transmission.
Comparative theoretical study of polarising panda type and microstructured fi...Kurbatov Roman
This document summarizes a comparative study of different types of polarizing fibres for use in fibre-optic gyroscopes (FOGs). It compares Panda-type fibres with W-index profiles and depressed cladding, as well as microstructured fibres. It analyzes the spectral width of their single-polarization windows while considering bending, and their splice losses when spliced to conventional fibres. A new type of match-clad Panda fibre that polarizes without bending is also proposed. Simulation methods are described for modeling the mechanical stresses and optical properties of the different fibre designs.
New optical w fiber panda for fiber optic gyroscope sensitive coilKurbatov Roman
This document proposes a new type of optical fiber called a W-fiber Panda that could improve fiber optic gyroscopes. The fiber has a core with nitrogen doping surrounded by stress-applying rods that create birefringence. Testing showed a polarizing version had 3 dB/km x-mode losses and 30 dB/km dichroism, while a polarization-maintaining version had ultra-low losses of 0.35 dB/km. This new fiber combines advantages of existing fibers by allowing a wide single-polarization spectral window as well as a desired mode field diameter. Its low losses could enable longer or more sensitive fiber optic gyroscope coils.
Optimization of Aberrated Coherent Optical SystemsIOSR Journals
This document summarizes research on optimizing the image quality of aberrated coherent optical systems through apodization. It studies how apodization filters can be used to reduce edge effects like ringing, gradient, and shifting caused by aberrations like defocus, coma, and spherical aberration. The results show that at certain apodization parameter values and aberration combinations, the image quality is improved with minimum edge shifting and improved edge gradient. Specifically, an apodization parameter of 0.75 eliminated edge ringing for various aberration combinations studied. Thus, apodization can help mitigate the degrading effects of one aberration through the introduction of other aberrations.
1) Using four laser beams, researchers generated a three-dimensional optical lattice that traps 490nm polystyrene spheres in solution, forming a face-centered orthorhombic crystal structure.
2) The four-beam setup produces a stable periodic potential in all three dimensions that counteracts particle diffusion via radiation pressure balance.
3) Calculations show the four-beam lattice with all beams polarized parallel produces a simple intensity pattern that yields a face-centered orthorhombic crystal structure when the beam angle is 45 degrees.
Fiber polarizer based on w lightguide pandaKurbatov Roman
This document summarizes the optical properties of three types of fiber polarizers based on panda-type W lightguides with different lengths: 200 m, 1 m, and 50 mm. For the 200 m and 1 m lightguides, dichroism (polarization dependent loss) is higher than 30 dB due to a difference in cutoff thresholds between the fundamental x and y modes. For the 50 mm lightguide, an additional scattering layer is included near the cladding boundary to achieve dichroism higher than 15 dB. The physical mechanisms behind the dichroism in each case are also described, including the effects of microbending and macrobending losses.
Theoretical study of metal clad optical waveguide polarizerijsrd.com
In this paper, the metal clad optical waveguide polarizer have been analysed and presented. The metal's that were used are Gallium Arsenide and Aluminium for the cladding purpose of comparison and analysis. It was found that the variation between TE mode and TM mode when Gallium Arsenide is used as the cladding is less as compared to Aluminium. This is due to the metal cladding itself will cause a cut-off region in the polarizer. Gallium arsenide may have fewer modes compared to aluminium and which resulted in the variation of the graphs between the two metals used. We have also shown that there is a slight drop of the TM to TE loss ratio when the buffer layer thickness is increased. It was also found that the high extinction ratio results in the high and linear attenuation in the fiber.
This document summarizes the research on reducing noise and vibration in flux switching permanent magnet (FSPM) machines. It proposes a method to estimate the circumferential mode frequencies of a segmented stator FSPM design using analytical models. It also proposes a pole shaping technique to reduce the effect of undesirable mode frequencies on noise and vibration. Finite element analysis was used to verify the analytical models. Testing of a prototype low-noise FSPM design showed improvements in reducing acoustic noise through increasing the dominant circumferential mode frequencies compared to a standard FSPM design.
This document describes how electric field gradients inside an atom interferometer can induce curvature in the de Broglie wavefront of atoms, leading to magnification and distortion of interference fringes. Simulations show that when the transverse coherence length of the atomic beam is shorter than the grating period, the fringes appear to fan out in different directions, an effect described as geometric magnification. Experiments demonstrate that in addition to shifting the phase of fringes, electrostatic lenses cause magnification and distortion of the fringes due to the induced curvature of the atomic de Broglie wavefront. An improved method of analyzing measurements of atomic beam velocity distributions using phase choppers is presented to account for this effect.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
This document presents a third order shear deformation theory to analyze flexure of thick cantilever beams. The theory uses a sinusoidal function in the displacement field to account for transverse shear deformation effects through the beam thickness. Governing equations and boundary conditions are derived using the principle of virtual work. Numerical examples of a cantilever beam with a cosine load distribution are presented and displacement, stress results are obtained in non-dimensional form. The results are discussed and compared to other beam theories to demonstrate the efficiency of the third order shear deformation theory.
New optical w fiber panda for fiber optic gyroscope sensitive coilKurbatov Roman
This document summarizes the proposal of a new type of optical fiber called a W profile Panda fiber that could address limitations of existing fiber types used in fiber optic gyroscope sensing coils. Key points:
- Existing fiber types used in sensing coils have losses over 1 dB/km which limits performance. A W profile Panda fiber is proposed to reduce losses through a core design that tightly confines the fundamental mode.
- The proposed fiber structure combines advantages of existing fiber designs to achieve both a wide single polarization spectral window for dichroism/polarization properties as well as control over the mode field diameter.
- Initial fibers produced based on the design achieved losses as low as 0.35 dB/km for a
This document analyzes the experimental measurement of bend loss in single mode and multimode optical fibers using an OTDR. The author measures bend loss at different bend radii and wavelengths. Results show that bend loss increases with decreasing bend radius and increasing wavelength. Bend loss is also higher in single mode fiber compared to multimode fiber for the same bend radius. The minimum bend radius before significant loss occurs is around 5mm. By measuring output power, the author shows that bend loss can be reduced at a radius of 11mm for single mode fiber and 12mm for multimode fiber.
This document is a summer internship report submitted by Prafull Kumar Sharma studying the depletion attraction between branched polymers using computer simulations. The report introduces the concepts of polymers, depletion attraction between colloids, dendrimer structure, and the bond fluctuation method used in the simulations. The goal is to understand depletion attraction between dendrimers with and without solvent using umbrella sampling to calculate free energy. Simulation results and their discussion are presented in section 3.
optical properties of dimer of plasmonic nanosphereAnuj012
The document discusses the optical properties of a dimer of plasmonic nanospheres using the multipole spectral expansion (MSE) method. MSE allows calculation of the potential at any point by separating geometric and dielectric properties, and can be extended to dimers and multimers. For a dimer, MSE derives matrix elements describing the interactions between the nanospheres. Translated eigenstates are also derived for each individual nanosphere. The method provides analytical results for the electric field enhancement in the gap between two closely spaced nanospheres.
Analytical approach to polarisation nonreciprocity of Sagnac fibre ring inter...Kurbatov Roman
- The document analyzes polarization nonreciprocity (PNR) in Sagnac fibre ring interferometers (FRIs), which are key components of fibre optic gyroscopes (FOGs).
- PNR arises from imperfections like slight rotations at splices between birefringent optical components in the FRI, as well as polarization mode coupling (PMC) in the coil fibre.
- The analysis derives an expression for PNR in terms of the coil fibre's birefringence, length, and spectral bandwidth of the light, which had not been consistently derived previously. It aims to do so using an analytical approach considering PMC in the coil fibre.
Higher-Order Squeezing of a Generic Quadratically-Coupled Optomechanical SystemIOSRJAP
Using short-time dynamics and analytical solution of Heisenberg equation of motion for the Hamiltonian of quadratically-coupled optomechanical system for different field modes, we have investigated the existence of higher-order single mode squeezing, sum squeezing and difference squeezing in absence of driving and dissipation. Depth of squeezing increases with order number for higher-order single mode squeezing. Squeezing factor exhibits a series of revival-collapse phenomena for single mode, which becomes more pronounced as order number increases. In case of sum squeezing amounts of squeezing is greater than single mode higher-order squeezing (n = 2). It is also greater than from difference squeezing for same set of interaction parameters. Sum squeezing is prominently better for extracting information regarding squeezing.
IRJET- Parabolic Loading in Fixed Deep Beam using 5th Order Shear Deformation...IRJET Journal
This document presents a study analyzing parabolic loading in fixed deep beams using a 5th order shear deformation theory. The authors develop a variationally consistent 5th order refined shear deformation theory for fixed-fixed beams. They obtain the governing differential equations and boundary conditions using the principle of virtual work. Numerical results are presented comparing displacements, stresses, and transverse shear stresses using the proposed 5th order theory versus higher-order plate and shear deformation theories and classical beam theory. The results show excellent agreement of the flexural stresses and shear stress distributions through the beam thickness between the proposed theory and other refined shear deformation theories. This validates the usefulness of the 5th order shear deformation theory.
Exciton localization in MgxZnyCd1–x–ySe alloyOleg Maksimov
The document summarizes photoluminescence and reflectivity measurements of MgxZnyCd1–x–ySe epitaxial layers with varying Mg content (x). As Mg content increases, significant emission line broadening, an increase in activation energy, and a large Stokes shift are observed. For samples with high Mg content (x > 0.3), an anomalous temperature dependence of emission energy and line broadening is seen, attributed to exciton localization. Exciton localization on statistical CdSe clusters within the alloy is proposed as the most likely localization mechanism.
This document presents an approach for modeling the propagation of light through stratified anisotropic media using Mueller matrices. It describes how to:
1) Set up the dielectric tensor in the laboratory frame using Euler rotations to relate the material and laboratory coordinate systems.
2) Calculate the propagation matrix Δ for each layer from the dielectric tensor and wavevector.
3) Determine the transition matrices at each interface by matching boundary conditions.
4) Obtain the Jones matrix for each layer and determine the overall Mueller matrix by matrix multiplication of the individual layer matrices.
This document analyzes how the mechanical properties of rubber coatings on inclusions influence wave propagation in acoustic metamaterials (AM). AM are composites that can attenuate waves at certain frequencies. The study models AM as periodic structures and finds that frequency gaps where waves are attenuated occur due to local resonance of inclusions vibrating at their resonant frequencies. Numerical results show that an incompressible rubber coating creates a single frequency gap at twice the frequency of the lowest gap for a compressible rubber coating. The conclusion is that the mechanical properties of rubber coatings significantly impact wave propagation characteristics in AM, and viscoelastic or nonlinear rubber behavior needs modeling for real AM.
Simulation of the different position on the E-type round diaphragm and the le...IOSR Journals
This document summarizes a study that simulates the effect of different positions and lengths of a beam resonator attached to an E-type round silicon diaphragm sensor for measuring acceleration. The sensor's sensing components are the diaphragm and attached beam. Finite element modeling is used to calculate the relationship between the beam's natural frequency and measured acceleration based on varying the beam's position on the diaphragm and length. The document provides background on resonant silicon sensors, describes the sensor's structure and sensing mechanism, analyzes stresses on the diaphragm, establishes mathematical models of the beam and diaphragm, and outlines the finite element modeling approach.
Plasmon-Polaritons And Their Use In Optical Sub-Wavelength. Event Of Copper A...ijrap
The work undertaken in this article concerns the description of the propagation modes of an incident
electromagnetic wave of wavelength λ (the visible spectrum) to its interaction with a structure typical metal
/ dielectric. The study of this interaction process is the measurement of features that are four parameters
associated with longitudinal modes propagating interface. A comparative study between two structures
silver and copper has been established. The characteristic parameters whose behavior is studied in the
visible spectrum are the propagation length, and the length of penetration in rural and dielectric material.
The typical structure of Kretschmann-Raether being used for the diagnosis of structure, analytical study
shows that copper can be used as a guide for photonic transmission. The direction of propagation, the
electromagnetic field associated with the interface modes present evanescent spatial coherence with which
the behavior is justified by a study of the near field. For this, we have given some results on the density of
states of plasmonic modes on a copper-air interface.
Survey paper on Virtualized cloud based IPTV Systemijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
A REVIEW PAPER ON EXPERIMENTAL AND NUMERICAL INVESTIGATION OF PARAMETRIC STUD...ijsrd.com
Combustion phenomena related to Froude number and Stroukal number were investigated in diffusion flames under various gravity levels. The Froude number of the fuel was controlled by gravity level, diameter of the nozzle, and fluid flow rate. Theoretical analysis is presented to laneway flame length model based on dimensional analyses. Analysis results indicate that flame length relates to heat release rate, fire source diameter, combustible matter diffusivity, etc. Based on Similarity principle, the laneway fire experiment plant has been setup. And using a video camera, the data of the experiment is recorded. Experiment results indicate that flame length is directly proportional to heat release rate, fire source diameter and combustible matter diffusivity. And a semi-empirical formula on flame length has been got using the least-square program to fit the experimental data. The results are of importance for flame radiation calculation and fire risk analysis. Flame is an important parameter for any combustion process which is responsible for either the complete or incomplete combustion process. There are certain factors which influence the flame length and diameter such as fire source diameter or nozzle diameter, equivalence ratio, quality of fuel, heat release rate etc. Investigation of flame length and diameter is more relevance in the rational design of combustion chamber, be it for an internal engine or for a furnace. The flame represents the zone of combustion, its length is a measure of the intensity of combustion and therefore of heat release. So, this paper reviews about the flame behavior on the basis of flame length and diameter.
Comparative Study on NDCT with Different Shell Supporting StructuresIJTET Journal
Natural draft cooling towers are very essential in modern days in thermal and nuclear power stations. These are the hyperbolic shells of revolution in form and are supported on inclined columns. Several types of shell supporting structures such as A,V,X,Y are being used for construction of NDCT’s. Wind loading on NDCT governs critical cases and requires attention. In this paper a comparative study on reinforcement details has been done on NDCT’s with X and Y shell supporting structures. For this purpose 166m cooling tower with X and Y supporting structures being analyzed and design for wind (BS & IS code methods), seismic loads using SAP2000.
Optimizing cloud resources for delivering iptv services through virtualizationMadan Golla
Cloud computing allows users to access data and applications from any device through the internet. It provides Infrastructure as a service (IaaS), Platform as a service (PaaS) and Software as a service (SaaS) through public, private or hybrid clouds. Internet Protocol television (IPTV) delivers video and audio over the internet to computers, televisions or mobile devices. The existing IPTV system has high server usage during instant channel changes but servers are idle at other times. A new system is proposed to dynamically shift resources between IPTV services using cloud computing and virtualization to better utilize servers.
Rostelecom replaced its aging IPTV platforms with a new cloud-based system to improve customer satisfaction and reduce costs. The multi-level architecture stores subscriber data, content, and preferences in the cloud for access across devices. Since launching in 2012, the service has grown from 500k to over 1.4 million subscribers, generating revenues that double yearly. Bundling interactive TV with broadband has reduced churn rates and increased average revenue per user through premium packages, video-on-demand, and multiroom services. The cloud-based platform positioned Rostelecom as the leading pay TV operator in Russia.
Correlation between cbr and index propertys of soilRAJESH JAIN
This document discusses correlations between the California Bearing Ratio (CBR) and index properties of soil. It examines several existing correlations between CBR and properties like liquid limit, plastic limit, and maximum dry density. The authors analyze data from previous studies to compare predicted CBR values from two correlations to experimentally measured CBR values. They find that one correlation works better for clayey soils but overestimates CBR for highly plastic clays, while the other correlation predicts lower CBR values than measured across soil types. The authors conclude that the correlations show some agreement with tests for low plasticity clays but need improvement to reliably predict CBR from simple soil properties.
This document summarizes the research on reducing noise and vibration in flux switching permanent magnet (FSPM) machines. It proposes a method to estimate the circumferential mode frequencies of a segmented stator FSPM design using analytical models. It also proposes a pole shaping technique to reduce the effect of undesirable mode frequencies on noise and vibration. Finite element analysis was used to verify the analytical models. Testing of a prototype low-noise FSPM design showed improvements in reducing acoustic noise through increasing the dominant circumferential mode frequencies compared to a standard FSPM design.
This document describes how electric field gradients inside an atom interferometer can induce curvature in the de Broglie wavefront of atoms, leading to magnification and distortion of interference fringes. Simulations show that when the transverse coherence length of the atomic beam is shorter than the grating period, the fringes appear to fan out in different directions, an effect described as geometric magnification. Experiments demonstrate that in addition to shifting the phase of fringes, electrostatic lenses cause magnification and distortion of the fringes due to the induced curvature of the atomic de Broglie wavefront. An improved method of analyzing measurements of atomic beam velocity distributions using phase choppers is presented to account for this effect.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
This document presents a third order shear deformation theory to analyze flexure of thick cantilever beams. The theory uses a sinusoidal function in the displacement field to account for transverse shear deformation effects through the beam thickness. Governing equations and boundary conditions are derived using the principle of virtual work. Numerical examples of a cantilever beam with a cosine load distribution are presented and displacement, stress results are obtained in non-dimensional form. The results are discussed and compared to other beam theories to demonstrate the efficiency of the third order shear deformation theory.
New optical w fiber panda for fiber optic gyroscope sensitive coilKurbatov Roman
This document summarizes the proposal of a new type of optical fiber called a W profile Panda fiber that could address limitations of existing fiber types used in fiber optic gyroscope sensing coils. Key points:
- Existing fiber types used in sensing coils have losses over 1 dB/km which limits performance. A W profile Panda fiber is proposed to reduce losses through a core design that tightly confines the fundamental mode.
- The proposed fiber structure combines advantages of existing fiber designs to achieve both a wide single polarization spectral window for dichroism/polarization properties as well as control over the mode field diameter.
- Initial fibers produced based on the design achieved losses as low as 0.35 dB/km for a
This document analyzes the experimental measurement of bend loss in single mode and multimode optical fibers using an OTDR. The author measures bend loss at different bend radii and wavelengths. Results show that bend loss increases with decreasing bend radius and increasing wavelength. Bend loss is also higher in single mode fiber compared to multimode fiber for the same bend radius. The minimum bend radius before significant loss occurs is around 5mm. By measuring output power, the author shows that bend loss can be reduced at a radius of 11mm for single mode fiber and 12mm for multimode fiber.
This document is a summer internship report submitted by Prafull Kumar Sharma studying the depletion attraction between branched polymers using computer simulations. The report introduces the concepts of polymers, depletion attraction between colloids, dendrimer structure, and the bond fluctuation method used in the simulations. The goal is to understand depletion attraction between dendrimers with and without solvent using umbrella sampling to calculate free energy. Simulation results and their discussion are presented in section 3.
optical properties of dimer of plasmonic nanosphereAnuj012
The document discusses the optical properties of a dimer of plasmonic nanospheres using the multipole spectral expansion (MSE) method. MSE allows calculation of the potential at any point by separating geometric and dielectric properties, and can be extended to dimers and multimers. For a dimer, MSE derives matrix elements describing the interactions between the nanospheres. Translated eigenstates are also derived for each individual nanosphere. The method provides analytical results for the electric field enhancement in the gap between two closely spaced nanospheres.
Analytical approach to polarisation nonreciprocity of Sagnac fibre ring inter...Kurbatov Roman
- The document analyzes polarization nonreciprocity (PNR) in Sagnac fibre ring interferometers (FRIs), which are key components of fibre optic gyroscopes (FOGs).
- PNR arises from imperfections like slight rotations at splices between birefringent optical components in the FRI, as well as polarization mode coupling (PMC) in the coil fibre.
- The analysis derives an expression for PNR in terms of the coil fibre's birefringence, length, and spectral bandwidth of the light, which had not been consistently derived previously. It aims to do so using an analytical approach considering PMC in the coil fibre.
Higher-Order Squeezing of a Generic Quadratically-Coupled Optomechanical SystemIOSRJAP
Using short-time dynamics and analytical solution of Heisenberg equation of motion for the Hamiltonian of quadratically-coupled optomechanical system for different field modes, we have investigated the existence of higher-order single mode squeezing, sum squeezing and difference squeezing in absence of driving and dissipation. Depth of squeezing increases with order number for higher-order single mode squeezing. Squeezing factor exhibits a series of revival-collapse phenomena for single mode, which becomes more pronounced as order number increases. In case of sum squeezing amounts of squeezing is greater than single mode higher-order squeezing (n = 2). It is also greater than from difference squeezing for same set of interaction parameters. Sum squeezing is prominently better for extracting information regarding squeezing.
IRJET- Parabolic Loading in Fixed Deep Beam using 5th Order Shear Deformation...IRJET Journal
This document presents a study analyzing parabolic loading in fixed deep beams using a 5th order shear deformation theory. The authors develop a variationally consistent 5th order refined shear deformation theory for fixed-fixed beams. They obtain the governing differential equations and boundary conditions using the principle of virtual work. Numerical results are presented comparing displacements, stresses, and transverse shear stresses using the proposed 5th order theory versus higher-order plate and shear deformation theories and classical beam theory. The results show excellent agreement of the flexural stresses and shear stress distributions through the beam thickness between the proposed theory and other refined shear deformation theories. This validates the usefulness of the 5th order shear deformation theory.
Exciton localization in MgxZnyCd1–x–ySe alloyOleg Maksimov
The document summarizes photoluminescence and reflectivity measurements of MgxZnyCd1–x–ySe epitaxial layers with varying Mg content (x). As Mg content increases, significant emission line broadening, an increase in activation energy, and a large Stokes shift are observed. For samples with high Mg content (x > 0.3), an anomalous temperature dependence of emission energy and line broadening is seen, attributed to exciton localization. Exciton localization on statistical CdSe clusters within the alloy is proposed as the most likely localization mechanism.
This document presents an approach for modeling the propagation of light through stratified anisotropic media using Mueller matrices. It describes how to:
1) Set up the dielectric tensor in the laboratory frame using Euler rotations to relate the material and laboratory coordinate systems.
2) Calculate the propagation matrix Δ for each layer from the dielectric tensor and wavevector.
3) Determine the transition matrices at each interface by matching boundary conditions.
4) Obtain the Jones matrix for each layer and determine the overall Mueller matrix by matrix multiplication of the individual layer matrices.
This document analyzes how the mechanical properties of rubber coatings on inclusions influence wave propagation in acoustic metamaterials (AM). AM are composites that can attenuate waves at certain frequencies. The study models AM as periodic structures and finds that frequency gaps where waves are attenuated occur due to local resonance of inclusions vibrating at their resonant frequencies. Numerical results show that an incompressible rubber coating creates a single frequency gap at twice the frequency of the lowest gap for a compressible rubber coating. The conclusion is that the mechanical properties of rubber coatings significantly impact wave propagation characteristics in AM, and viscoelastic or nonlinear rubber behavior needs modeling for real AM.
Simulation of the different position on the E-type round diaphragm and the le...IOSR Journals
This document summarizes a study that simulates the effect of different positions and lengths of a beam resonator attached to an E-type round silicon diaphragm sensor for measuring acceleration. The sensor's sensing components are the diaphragm and attached beam. Finite element modeling is used to calculate the relationship between the beam's natural frequency and measured acceleration based on varying the beam's position on the diaphragm and length. The document provides background on resonant silicon sensors, describes the sensor's structure and sensing mechanism, analyzes stresses on the diaphragm, establishes mathematical models of the beam and diaphragm, and outlines the finite element modeling approach.
Plasmon-Polaritons And Their Use In Optical Sub-Wavelength. Event Of Copper A...ijrap
The work undertaken in this article concerns the description of the propagation modes of an incident
electromagnetic wave of wavelength λ (the visible spectrum) to its interaction with a structure typical metal
/ dielectric. The study of this interaction process is the measurement of features that are four parameters
associated with longitudinal modes propagating interface. A comparative study between two structures
silver and copper has been established. The characteristic parameters whose behavior is studied in the
visible spectrum are the propagation length, and the length of penetration in rural and dielectric material.
The typical structure of Kretschmann-Raether being used for the diagnosis of structure, analytical study
shows that copper can be used as a guide for photonic transmission. The direction of propagation, the
electromagnetic field associated with the interface modes present evanescent spatial coherence with which
the behavior is justified by a study of the near field. For this, we have given some results on the density of
states of plasmonic modes on a copper-air interface.
Survey paper on Virtualized cloud based IPTV Systemijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
A REVIEW PAPER ON EXPERIMENTAL AND NUMERICAL INVESTIGATION OF PARAMETRIC STUD...ijsrd.com
Combustion phenomena related to Froude number and Stroukal number were investigated in diffusion flames under various gravity levels. The Froude number of the fuel was controlled by gravity level, diameter of the nozzle, and fluid flow rate. Theoretical analysis is presented to laneway flame length model based on dimensional analyses. Analysis results indicate that flame length relates to heat release rate, fire source diameter, combustible matter diffusivity, etc. Based on Similarity principle, the laneway fire experiment plant has been setup. And using a video camera, the data of the experiment is recorded. Experiment results indicate that flame length is directly proportional to heat release rate, fire source diameter and combustible matter diffusivity. And a semi-empirical formula on flame length has been got using the least-square program to fit the experimental data. The results are of importance for flame radiation calculation and fire risk analysis. Flame is an important parameter for any combustion process which is responsible for either the complete or incomplete combustion process. There are certain factors which influence the flame length and diameter such as fire source diameter or nozzle diameter, equivalence ratio, quality of fuel, heat release rate etc. Investigation of flame length and diameter is more relevance in the rational design of combustion chamber, be it for an internal engine or for a furnace. The flame represents the zone of combustion, its length is a measure of the intensity of combustion and therefore of heat release. So, this paper reviews about the flame behavior on the basis of flame length and diameter.
Comparative Study on NDCT with Different Shell Supporting StructuresIJTET Journal
Natural draft cooling towers are very essential in modern days in thermal and nuclear power stations. These are the hyperbolic shells of revolution in form and are supported on inclined columns. Several types of shell supporting structures such as A,V,X,Y are being used for construction of NDCT’s. Wind loading on NDCT governs critical cases and requires attention. In this paper a comparative study on reinforcement details has been done on NDCT’s with X and Y shell supporting structures. For this purpose 166m cooling tower with X and Y supporting structures being analyzed and design for wind (BS & IS code methods), seismic loads using SAP2000.
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Paper theoretical and experimental studies of lamb wave propagation in attenuative composites
1. Theoretical and experimental studies of Lamb wave propagation
in attenuative composites
Mircea Calomfirescu*ab
, Axel S. Herrmanna
a
Faserinstitut Bremen e.V., University of Bremen, Am Biologischen Garten 2, Bremen, Germany
b
University of South Carolina, 300 Main St., Columbia, SC, USA 29208
ABSTRACT
This paper presents a theoretical model for anisotropic wave attenuation in composites. The model has been
implemented in a software called FIBREWAVE in order to predict dispersion and attenuation of S0, A0 and SH0 Lamb
wave modes. The required input data are the complex stiffness matrix coefficients of the unidirectional plies of the
laminate, which have been measured by a laser interferometry method. Complex stiffness data for an unidirectional
CFRP laminates are moreover presented. Satisfactory agreement has been observed between predicted and experimental
group velocities and wave attenuations.
Keywords: Lamb waves, Composites, Viscoelastic Properties, SHM, Wave Attenuation, Damping
.
1. INTRODUCTION
In order to ensure structural integrity and maintain safety aerospace structures have to be inspected. At the present time
there is a variety of non-destructive, traditional inspection techniques (NDT) available such as eddy current, ultrasonics,
thermography and shearography [1]. The major disadvantages of these techniques are related to high (life-cycle) cost,
damage detection sensitivity, time consuming and require the structure to be out of service. Recent years have shown a
range of different NDT for so called “structural health monitoring (SHM)”, which consists of two different approaches:
passive sensing monitoring and active sensing monitoring. The active approach needs both sensors and actuators to
evaluate and monitor the structural health. The passive technique needs only sensors to collect data of structural waves
excited by an external source, such as an impact or a propagating crack. Various SHM systems based on different types
of sensors such as piezoelectric elements, fibre optics and MEMS sensors has already been developed and presented in
laboratory demonstrations at meetings and workshops [2-5]. Most of the presented SHM techniques [6-7], require
experimental training data sets to determine the relation between force histories and the corresponding strain responses
or between failures and sensor signals. Such techniques would benefit of improved theoretical understanding of wave
propagation in anisotropic composites to construct a precise analytical/numerical model without conducting numerous
experimental tests. A crucial element in the Lamb wave propagation in composites is the wave attenuation. The
fundamental understanding and prediction of the anisotropic wave attenuation could be then applied for:
- the design of sensor networks (number and location of sensors), since the material attenuation decides in the
far field how far waves can travel and can be still detected
- the detection of damage, since the attenuation characteristics of a structure increase in general in the presence
of damage [8]
- the prediction of an impact load in impact identification methods, since the amplitude of the measured stress
waves decays depending on the distance between the impact and the location of the sensor.
Therefore the objective of our research was to develop a theoretical model, enabling the prediction of the dispersion and
attenuation behavior in composites with arbitrary lay-ups. The developed theoretical model has been implemented in a
MatLab software and verified by experiments. The material characterization has been conducted at the Laboratoire de
Mecanique Physique (LMP) at the University of Bordeaux [9].
*calomfirescu@faserinstitut.de; phone +49 421 218 9335; fax +49 421 218 3110
2. 2. LAMB WAVES IN COMPOSITES
Lamb waves are a type of ultrasonic waves, which are also known as guided plate waves, due to the fact that they are
guided between two parallel free surfaces, the upper and the lower surface of the plate [13]. For each frequency more
than one wave modes exists. In composites these wave modes are at low frequencies S0, A0 and SH0, the latter one,
denoting the shear horizontal wave. The symmetrical modes are called, S0, S1, S2,…, and the anti-symmetric ones A0,
A1, A2…, starting with the mode that has the lowest frequency for a given wavenumber.
Fig. 1: Low order Lamb wave modes
2.1 Attenuation of Lamb waves
The definition of attenuation in general is the loss of amplitude of an acoustic wave with propagation distance. In the
case of omnidirectional excited waves, there are, as discussed by [11], four main contributing factors: geometric
spreading, material damping, wave dissipation into adjacent media and losses related to velocity dispersion. In the near
field, close to the source, the geometric spreading is the dominant source for wave attenuation, where for plate-like
structures and a point-wise excitation source, the wave amplitude decreases inversely as the square root of the distance
of propagation. The second factor, which is the dominating influence in the far field and the factor to be most discussed
in this paper is the material damping. Here energy is converted into heat and thus extract from the mechanical system.
The last but one attenuation mechanism is related to energy losses into adjacent media, like from a vessel into the
contained fluid are structural attenuation at stiffeners and joints. The final attenuation mechanism, the attenuation due to
dispersion, as well as the last but one mechanisms can be neglected in these studies, since here narrow band, single
frequency Lamb waves for simple structures are considered.
Due to the high material damping, attenuation leads to a decay of the amplitude of Lamb waves in composites much
stronger that in metallic structures. Attenuation is crucial for the wave propagation and detection, since it decides how
far Lamb waves modes can be transmitted with a sufficient signal to noise ratio. Moreover a change in stress wave
attenuation can be used for damage detection, since attenuation increases in the presence of material damages [8].
Besides of the frequency and Lamb wave mode dependency, attenuation in composites is anisotropic, depending on the
direction of wave propagation.
In this research the viscoelastic behavior of the composites is taken into account by considering complex components in
the material’s stiffness matrix of each unidirectional (UD)- ply:
ijijij CiCC ′′⋅+′=*
(1)
where ijC′ contains the storage moduli and
″
ijC the loss moduli. In order to consider arbitrary laminates with UD-plies
layed up in different angles, the stiffness matrix of each ply ( ∗
ijC ) has to be polar transformed in the coordinate system
of the laminate ( *~
ijC ) . Moreover, the complex wave number is introduced and defined by:
kikk ′′⋅+′=*
, (2)
where k ′′ represents the attenuation coefficient with units of dB/unit distance. Thus, a hysteretic model [12] is
considered in this study to represent material damping.
3. The complex stiffness matrix of the laminate according to the applied higher order theory has the form:
(3)
where the coefficients can be obtained by the lamination theory as follows:
/2
* * * * * * 2 3 4
/2
( , , , , ) ( ) (1, , , , )
h
ij ij ij ij ij k
h
A B D F H Q ij z z z z dz
−
= ∫ , (4)
The
*
Q ij terms are the complex reduced stiffness coefficients of each unidirectional ply as defined by:
* *
* *
*
( ,3) (3, )
(3,3)
ij ij
ij ij
ij
C i C j
Q C
C
⎛ ⎞⎛ ⎞⋅
= −⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟
⎝ ⎠⎝ ⎠
(5)
The usual coupling between antisymmetric and symmetric modes for a laminate of arbitrary stacking sequence is given
through the stiffness Bij and Fij. In this study these stiffness coefficients are not taken into account. By applying this
simplification only symmetrical lamintes can be calculated by our approach. With the linear strain-displacement
relations, the equations of motion of the higher-order theory can be derived using the principle of virtual displacement
or Hamilton’s principle. After formulation the equations of motions and assuming the solution form as
( )* *
0 0
x y
i k x k y t
u U e
ω⎡ ⎤⋅ + ⋅ −
⎢ ⎥⎣ ⎦
= ,
( )* *
0 0
x y
i k x k y t
v V e
ω⎡ ⎤⋅ + ⋅ −
⎢ ⎥⎣ ⎦
= ,
( )* *
0 0
x y
i k x k y t
w W e
ω⎡ ⎤⋅ + ⋅ −
⎢ ⎥⎣ ⎦
= ,
( )* *
x y
i k x k y t
x xe
ω
ψ
⎡ ⎤⋅ + ⋅ −
⎢ ⎥⎣ ⎦
= Ψ (6)
( )* *
x y
i k x k y t
y ye
ω
ψ
⎡ ⎤⋅ + ⋅ −
⎢ ⎥⎣ ⎦
= Ψ ,
( )* *
x y
i k x k y t
z ze
ω
ψ
⎡ ⎤⋅ + ⋅ −
⎢ ⎥⎣ ⎦
= Ψ ,
( )* *
x y
i k x k y t
x xe
ω
φ
⎡ ⎤⋅ + ⋅ −
⎢ ⎥⎣ ⎦
= Φ ,
( )* *
x y
i k x k y t
y ye
ω
φ
⎡ ⎤⋅ + ⋅ −
⎢ ⎥⎣ ⎦
= Φ
the following relation is obtained:
4. 0
0
0
0
0
0
88
7877
686766
58575655
4847464544
383736353433
281826252422
18171615141211
=
⎪
⎪
⎪
⎪
⎪
⎭
⎪
⎪
⎪
⎪
⎪
⎬
⎫
⎪
⎪
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎪
⎪
⎨
⎧
Φ
Φ
Ψ
Ψ
Ψ
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
y
x
z
y
x
W
V
U
L
LL
LLLsym
LLLL
LLLLL
LLLLLL
LLLLLL
LLLLLLL
(7)
The coefficients Lij are a function of the complex stiffness matrix coefficients from equation (3), the wave number and
the frequency. For symmetric laminates equation (7) can be decoupled into symmetric waves:
0
0
0
88
7877
686766
28182622
1817161211
=
⎪
⎪
⎪
⎭
⎪⎪
⎪
⎬
⎫
⎪
⎪
⎪
⎩
⎪⎪
⎪
⎨
⎧
Φ
Φ
Ψ
⎥
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎣
⎡
y
x
z
V
U
L
LLsym
LLL
LLLL
LLLLL
(8)
and antisymmetric waves:
0
0
55
4544
353433
=
⎪
⎭
⎪
⎬
⎫
⎪
⎩
⎪
⎨
⎧
Ψ
Ψ
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
y
x
W
Lsym
LL
LLL
(9)
Each root of these relations is related to a certain Lamb-wave mode, for which the dispersian and attenuation
characteristics can be then obtained.
3. SOFTWARE
To gain better understanding of wave propagation and attenuation in composites the theoretic model has been put into
mathematics software. The software was developed in a MatLab environment and predicts the dispersion and
attenuation behavior for composites with arbitrary lay-ups. As input data the complex stiffness matrix of each UD-ply,
the lay-up and the thickness of each ply has to be given. Fig. 2 shows the front panel of the software called
FIBREWAVE, and developed at the Faserinstitut Bremen.
5. Fig. 2: GUI of the software FIBREWAVE
Additional outputs of the software are polar plots for phase and group velocities and attenuation plots at arbitrary
frequencies.
4. MEASUREMENTS
For applying the described theoretical model for the prediction of the dispersion and attenuation behavior the
components of the viscoelastic stiffness matrix of the CFRP laminates has to be investigated. In this study the properties
have been measured at the Laboratoire de Mecanique Physique (LMP) of the University of Bordeaux. The immersion
technique has been developed in the 90’s at by the LMP and described in detail in [9]. The principle of this method
consists in sending and receiving an ultrasonic plane field. The frequency bandwith has to be chosen so that the material
is seen by the waves as a homogeneous medium. The material properties are then obtained numerically inverting the
transmitted ultrasonic fields, obtained for different incident angles.
The viscoelastic stiffness properties (Cij) obtained and used for a 5.1 mm thick unidirectional carbon-epoxy laminate
are shown in table 1.
C11 C22 C33 C12 C13 C23 C44 C55 C66
C’ij 125 ± 8
13.9 ± 0.4
14.5 ± 0.4
6.3 ± 0.6
5.4± 0.4
7.1 ± 0.2
3.7 ± 0.3
5.4 ± 0.4
5.4 ± 0.6
C’’ij 3 ± 1
0.6 ± 0.2
0.6 ± 0.2
0.9 ± 0.6
0.4 ± 0.2
0.23 ± 0.15
0.12 ± 0.06
0.3 ± 0.15
0.5 ± 0.25
Table 1: Results of Cij (in GPa) for the unidirectional CFRP laminate
The intervals of errors obtained with this technique are quite standard for this type of material. Also usual is the fact that
the relative errors are much bigger for the imaginary parts of the stiffness coefficients than for the real parts. The
imaginary part of C11 is particularly hard to measure.
In order to verify the mathematical model and the developed software, experimental pitch-catch measurements have
been performed. The experimental setup consists of a CFRP plate with the overall dimensions of 500 x 500 mm. The
plate was instrumented with piezoelectric waver active sensors (PWAS) with a diameter of 7 mm and a thickness of 200
µm from American Piezo Ceramics APC-850. A 4-channel digital oscilloscope was used to collect the signals from the
PWAS. For collecting dispersion and attenuation data in three propagation angles (0°, 45° and 90°) the experimental
6. setup illustrated in Fig. 3 has been employed. A total number of 10 round PWAS has been applied. In the configuration
illustrated in Fig. 3 PWAS #1 excites waves, which are then collected at the sensors #2, #3 and #4, for 0° propagation.
Fig. 3: Experimental Setup for Lamb wave propagation
The distance between PWAS #1 and #2 was 149 mm, that between #2 and #3, 130 mm and between PWAS #3 and #4,
69 mm. Thus, with this sensor configuration the propagation characteristics in 0°- direction can be analyzed. For the
Lamb wave excitation an HP33120A arbitrary signal generator was used. The excitation applied was a 3-count tone-
burst signal filtered through a Hanning window to excite coherent single-frequency waves [13]. For the measurements
of wave velocities at different frequencies the corresponding times of flight (TOF) has been analyzed. As arrival time
the maximum of the magnitude of the continuous wavelet transform (CWT) coefficients for the corresponding
excitation scale has been used. By this approach it was possible to obtain a clean, smooth envelope, since only the
excitation frequency is considered. The Gabor function was used as mother wavelet. For the experimental evaluation of
material attenuation the phenomenon of geometric spreading was taken into account by correcting the amplitude
decrease in order to obtain the decay due to material damping only. The decrease of wave amplitude due to geometric
spreading has been corrected by the relation 1 d , where d is the distance between the location the amplitudes have
been collected.
Fig. 4 illustrates the wave propagation at 80 kHz center frequency excitation for the 90° propagation direction (matrix
direction). At this frequency the both Lamb waves modes S0 and the A0 can be excited and recognized and distinguished
clearly. The very first, highest peak has to be neglected since it comes from the electro- mechanical coupling and does
not denote any Lamb wave mode. The first Lamb wave signal arriving at the PWAS # 8 at t = 63 µs corresponds to the
S0 symmetrical mode, the latter, arriving at t = 109 µs corresponds to the A0 mode. The attenuation coefficient in
dB/unit distance can be then calculated by the relation of the amplitude ratios and distances according to:
[ ]
2 2
1 1
2 1
ln
20 log
A d
A d
d d
k dB mm e
⎛ ⎞
⋅⎜ ⎟⎜ ⎟
⎝ ⎠−
−
⎛ ⎞
⎜ ⎟
⎜ ⎟′′ = ⋅
⎜ ⎟
⎜ ⎟
⎝ ⎠
(10)
where d1 and d2 are the distances from the excitation source, and A1 and A2 the collected amplitudes. The factor
2 1d d is the correction factor taking into account the geometric spreading due to the point source excitation.
7. Fig. 4: Wave propagation in 90° laminate direction (at 80 kHz)
This single frequency excitation has been performed from 5 kHz to 400 kHz each 10 kHz. Since not for all excitation
frequencies all Lamb wave modes can be clearly and strongly excited and in additionally many cases the measurements
are disturbed by reflections from boundaries not for all frequencies could be performed reliable measurements. Fig. 5
and 6 show the dispersion and attenuation data obtained by the described experimental pitch-catch measurements and
plotted against theoretical, by FIBREWAVE predicted values.
Fig. 5: Predicted and measured dispersion and attenuation for 0° wave propagation in an unidirectional CFRP laminate
The experimental dispersion values for the A0 mode as well as the attenuation of this Lamb wave mode could be
extracted much more reliable than those of the S0 mode for two reasons. Due to the high wave velocity in fibre direction
(~ 9000 m/s for low frequencies) the various echoes between the edges of the 500 mm long sample are too close to each
other in the dime domain, thus preventing to obtain an accurate estimation of its attenuation. Therefore a layer of clay
has been applied on the CFRP plate at the boundaries in order to reduce boundary reflections. Although the application
of clay reduced the reflections significantly, it was still not possible for the relatively small plate to extract reliable
attenuation values for the S0 mode. Despite some uncertainties satisfactory agreement has been observed for the A0
mode for the dispersion as well as for the attenuation behavior. For higher frequencies beyond 180 kHz the A0 mode
could not be excited strongly enough, so that no experimental values are available for this range. Moreover the SH0
mode could not be detected reliably.
Fig. 6 shows the dispersion and attenuation characteristics of the same CFRP unidirectional plate for 90° Lamb wave
propagation. As expected and predicted it shows clearly the lower propagation velocity for A0 and S0 modes in 90°
8. propagation direction in comparison to the 0° direction (fibre direction). In Fig. 6 right the attenuation is plotted against
frequency for the Lamb wave modes A0 and S0. Since in general, as for the most of the previously analyzed CFRP-
laminates observed, the attenuation of S0 is lower than that of A0, for this laminate it is contrary for frequencies beyond
~40 kHz.
Fig. 6: Predicted and measured dispersion and attenuation for 90° wave propagation in an unidirectional CFRP laminate
5. SUMMARY AND CONCLUSIONS
A theoretical model for the propagation of S0, A0 and SH0 modes in viscoelastic composites has been developed and
implemented in a software called FIBREWAVE enabling the prediction of dispersion and attenuation behavior in
composites with arbitrary lay-ups. The viscoelastic (complex) material properties used have been measured by a laser
interferometry method at the University of Bordeaux. Besides some uncertainties good agreement between the
experimental and the predicted values has been observed showing the high wave attenuation in composites in
comparison to metallic structures.
The highly attenuative and anisotropic behavior of composites has to be taken into account for SHM applications in
future studies since it defines how far waves can travel in different directions. In the next steps, after fully experimental
confirmation on much more laminates with different lay-ups, the model will be implemented in the explicit finite-
element code LS-DYNA, which has already been applied and extensively validated at the Faserinstitut Bremen for wave
propagation analysis. The developed attenuation model in combination with a FEA-based optimization method will be
then applied for design optimal sensor network (no. and location of sensors) for more complex structure. Last but not
least viscoelastic material characterization will be conducted with surface bonded PWAS.
ACKNOWLEDGMENTS
The financial support of this research by a grant from the DFG (Deutsche Forschungsgemeinschaft) is gratefully
appreciated. Moreover the author would like to thank Professor Giurgiutiu from the Laboratory for Active Materials and
Smart Structures (LAMSS) at the University of South Carolina for the benefit of his research environment and
interactions and Professor Castaings from Laboratoire de Mecanique Physique (LMP) at the University of Bordeaux for
the material characterization.
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