1) The document describes modeling of elastic wave propagation in thin plate structures using spectral element method. Spectral elements use higher order polynomials which allow for accurate modeling of high frequency elastic waves with wavelengths of 13-38 mm in plates that are 1-2 mm thick.
2) A 36 node spectral plate element is formulated using Mindlin-Reissner plate theory and Gauss-Lobatto-Legendre polynomials. Wave propagation is simulated in a clamped square plate excited by a unit load to demonstrate the method.
3) The spectral element method converges faster than finite element method for modeling high frequency elastic wave propagation, with fewer degrees of freedom needed for the same accuracy. This allows for efficient modeling of structural
Buckling of a carbon nanotube embedded in elastic medium via nonlocal elastic...IRJESJOURNAL
Abstract:- Buckling analysis of a carbon nanotube (CNT) embedded in Pasternak’s medium is investigated. Eringen’s nonlocal elasticity theory in conjunction with the first-order Donell’s shell theory is used. The governing equilibrium equations are obtained and solved for CNTs subjected to mechanical loads and embedded in Winkler-Pasternak’s medium. Effects of nonlocal parameter, radius and length of CNT, as well as the foundation parameters on buckling of CNT are investigated. Comparison with the available results is made.
A pictorial method of visualizing curl & determinant operation utilized i...ijscmcj
Curl and Determinant operations are well known in the field of Electromagnetics and fluid dynamics. Famous Maxwell’s equations involve curl operation. Though this operation is widely used to represent rotation, we do not have sufficient literature explaining how this operation represents rotation.
Most of the books omit detailed discussion on the physical interpretation of the Curl and Determinan operation. In this paper we have attempted to develop a pictorial method to provide a logical proof showing the versatility of this operation to study the rotating vectors. We further show how this pictorial method simplifies the fundamental expression with regard to determinants.
We cover the inverses to the trigonometric functions sine, cosine, tangent, cotangent, secant, cosecant, and their derivatives. The remarkable fact is that although these functions and their inverses are transcendental (complicated) functions, the derivatives are algebraic functions. Also, we meet my all-time favorite function: arctan.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Buckling of a carbon nanotube embedded in elastic medium via nonlocal elastic...IRJESJOURNAL
Abstract:- Buckling analysis of a carbon nanotube (CNT) embedded in Pasternak’s medium is investigated. Eringen’s nonlocal elasticity theory in conjunction with the first-order Donell’s shell theory is used. The governing equilibrium equations are obtained and solved for CNTs subjected to mechanical loads and embedded in Winkler-Pasternak’s medium. Effects of nonlocal parameter, radius and length of CNT, as well as the foundation parameters on buckling of CNT are investigated. Comparison with the available results is made.
A pictorial method of visualizing curl & determinant operation utilized i...ijscmcj
Curl and Determinant operations are well known in the field of Electromagnetics and fluid dynamics. Famous Maxwell’s equations involve curl operation. Though this operation is widely used to represent rotation, we do not have sufficient literature explaining how this operation represents rotation.
Most of the books omit detailed discussion on the physical interpretation of the Curl and Determinan operation. In this paper we have attempted to develop a pictorial method to provide a logical proof showing the versatility of this operation to study the rotating vectors. We further show how this pictorial method simplifies the fundamental expression with regard to determinants.
We cover the inverses to the trigonometric functions sine, cosine, tangent, cotangent, secant, cosecant, and their derivatives. The remarkable fact is that although these functions and their inverses are transcendental (complicated) functions, the derivatives are algebraic functions. Also, we meet my all-time favorite function: arctan.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Numerical simulation on laminar convection flow and heat transfer over a non ...eSAT Journals
Abstract
A numerical algorithm is presented for studying laminar convection flow and heat transfer over a non-isothermal horizontal plate.
plate temperature Tw varies with x in the following prescribed manner:
T T Cx w
n 1
where C and n are constants. By means of similarity transformation, the original nonlinear partial differential equations of flow
are transformed to a pair of nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and
integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical
analysis in Matlab environment. Velocity, and temperature profiles for various Prandtl number and n are illustrated graphically.
Flow and heat transfer parameters are derived. The results of the present simulation are then compared with experimental data in
literature with good agreement.
Keywords: Free Convection, Heat Transfer, Non-isothermal Horizontal Plate, Matlab, Numerical Simulation.
An Asymptotic Approach of The Crack Extension In Linear PiezoelectricityIRJESJOURNAL
Abstract: As a result of a theoretical technique for elucidating the fracture mechanics of piezoelectric materials, this paper provides, on the basis of the three-dimensional model of thin plates, an asymptotic behavior in the Griffith’s criterion for a weakly anisotropic thin plate with symmetry of order six, through a mathematical analysis of perturbations due to the presence of a crack. It is particularly established, in this work, the effects of both electric field and singularity of the in-plane mechanical displacement on the piezoelectric energy
NANO106 is UCSD Department of NanoEngineering's core course on crystallography of materials taught by Prof Shyue Ping Ong. For more information, visit the course wiki at http://nano106.wikispaces.com.
A numerical solution for Sine-Gordon type system was done by the use of two finite difference schemes, the first is the explicit scheme and the second is the Crank-Nicholson scheme. A comparison between the two schemes showed that the explicit scheme is easier and has faster convergence than the Crank-Nicholson scheme which is more accurate. The MATLAB environment was used for the numerical computations.
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
Weighted Analogue of Inverse Maxwell Distribution with ApplicationsPremier Publishers
In the present study, we established a new statistical model named as weighted inverse Maxwell distribution (WIMD). Its several statistical properties including moments, moment generating function, characteristics function, order statistics, shanon entropy has been discussed. The expression for reliability, mode, harmonic mean, hazard rate function has been derived. In addition, it also contains some special cases that are well known. Moreover, the behavior of probability density function (p.d.f) has been shown through graphs by choosing different values of parameters. Finally, the performance of the proposed model is explained through two data sets. By which we conclude that the established distribution provides better fit.
Optimization of technological process to decrease dimensions of circuits xor ...ijfcstjournal
The paper describes an approach of increasing of integration rate of elements of integrated circuits. The
approach has been illustrated by example of manufacturing of a circuit XOR. Framework the approach one
should manufacture a heterostructure with specific configuration. After that several special areas of the
heterostructure should be doped by diffusion and/or ion implantation and optimization of annealing of dopant
and/or radiation defects. We analyzed redistribution of dopant with account redistribution of radiation
defects to formulate recommendations to decrease dimensions of integrated circuits by using analytical
approaches of modeling of technological process.
Muravin The fundamentals of Structural Health Monitoring using Acoustic Emis...mboria
Structural Health Monitoring (SHM) is an emerging field of modern engineering that deals with diagnosis and monitoring of structures during their operation. Increasing requirements for safety, development of tools and criteria for condition based maintenance (CBM), cost reduction are all driving development of SHM methods in different industries. The primary goal of SHM is detection, identification, assessment and monitoring of flaws or faults/conditions that affect or may affect in a future safety or performance of structures. SHM combines elements of non-destructive testing and evaluation, condition/process monitoring, statistical pattern recognition and physical modeling. Acoustic emission method uniquely fits to the concept of SHM due to its capabilities to examine, monitor structures and assess structural integrity during their normal operation.
In this work, the fundamental definitions and principles of application of Acoustic Emission as a method of SHM are elaborated. This includes:
• Recommended terminology and definitions of SHM by the AE method.
• Outline of recommended process of AE SHM.
• Fundamental assumptions and principals regarding development of new SHM procedures, selection of equipment and methods of data acquisition and analysis, diagnosis, monitoring and prediction by AE SHM.
The developed principals provide an outline for systematic and standard development of new SHM applications based on Acoustic Emission method.
Numerical simulation on laminar convection flow and heat transfer over a non ...eSAT Journals
Abstract
A numerical algorithm is presented for studying laminar convection flow and heat transfer over a non-isothermal horizontal plate.
plate temperature Tw varies with x in the following prescribed manner:
T T Cx w
n 1
where C and n are constants. By means of similarity transformation, the original nonlinear partial differential equations of flow
are transformed to a pair of nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and
integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical
analysis in Matlab environment. Velocity, and temperature profiles for various Prandtl number and n are illustrated graphically.
Flow and heat transfer parameters are derived. The results of the present simulation are then compared with experimental data in
literature with good agreement.
Keywords: Free Convection, Heat Transfer, Non-isothermal Horizontal Plate, Matlab, Numerical Simulation.
An Asymptotic Approach of The Crack Extension In Linear PiezoelectricityIRJESJOURNAL
Abstract: As a result of a theoretical technique for elucidating the fracture mechanics of piezoelectric materials, this paper provides, on the basis of the three-dimensional model of thin plates, an asymptotic behavior in the Griffith’s criterion for a weakly anisotropic thin plate with symmetry of order six, through a mathematical analysis of perturbations due to the presence of a crack. It is particularly established, in this work, the effects of both electric field and singularity of the in-plane mechanical displacement on the piezoelectric energy
NANO106 is UCSD Department of NanoEngineering's core course on crystallography of materials taught by Prof Shyue Ping Ong. For more information, visit the course wiki at http://nano106.wikispaces.com.
A numerical solution for Sine-Gordon type system was done by the use of two finite difference schemes, the first is the explicit scheme and the second is the Crank-Nicholson scheme. A comparison between the two schemes showed that the explicit scheme is easier and has faster convergence than the Crank-Nicholson scheme which is more accurate. The MATLAB environment was used for the numerical computations.
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
Weighted Analogue of Inverse Maxwell Distribution with ApplicationsPremier Publishers
In the present study, we established a new statistical model named as weighted inverse Maxwell distribution (WIMD). Its several statistical properties including moments, moment generating function, characteristics function, order statistics, shanon entropy has been discussed. The expression for reliability, mode, harmonic mean, hazard rate function has been derived. In addition, it also contains some special cases that are well known. Moreover, the behavior of probability density function (p.d.f) has been shown through graphs by choosing different values of parameters. Finally, the performance of the proposed model is explained through two data sets. By which we conclude that the established distribution provides better fit.
Optimization of technological process to decrease dimensions of circuits xor ...ijfcstjournal
The paper describes an approach of increasing of integration rate of elements of integrated circuits. The
approach has been illustrated by example of manufacturing of a circuit XOR. Framework the approach one
should manufacture a heterostructure with specific configuration. After that several special areas of the
heterostructure should be doped by diffusion and/or ion implantation and optimization of annealing of dopant
and/or radiation defects. We analyzed redistribution of dopant with account redistribution of radiation
defects to formulate recommendations to decrease dimensions of integrated circuits by using analytical
approaches of modeling of technological process.
Muravin The fundamentals of Structural Health Monitoring using Acoustic Emis...mboria
Structural Health Monitoring (SHM) is an emerging field of modern engineering that deals with diagnosis and monitoring of structures during their operation. Increasing requirements for safety, development of tools and criteria for condition based maintenance (CBM), cost reduction are all driving development of SHM methods in different industries. The primary goal of SHM is detection, identification, assessment and monitoring of flaws or faults/conditions that affect or may affect in a future safety or performance of structures. SHM combines elements of non-destructive testing and evaluation, condition/process monitoring, statistical pattern recognition and physical modeling. Acoustic emission method uniquely fits to the concept of SHM due to its capabilities to examine, monitor structures and assess structural integrity during their normal operation.
In this work, the fundamental definitions and principles of application of Acoustic Emission as a method of SHM are elaborated. This includes:
• Recommended terminology and definitions of SHM by the AE method.
• Outline of recommended process of AE SHM.
• Fundamental assumptions and principals regarding development of new SHM procedures, selection of equipment and methods of data acquisition and analysis, diagnosis, monitoring and prediction by AE SHM.
The developed principals provide an outline for systematic and standard development of new SHM applications based on Acoustic Emission method.
Smart Sensors for Infrastructure and Structural Health MonitoringJeffrey Funk
These slides use concepts from my (Jeff Funk) course entitled analyzing hi-tech opportunities to show how smart sensors are becoming more economically feasible and more widely used in infrastructure. This is enabling greater monitoring and self-healing of structures. Twenty years ago, it was improvements in MEMS, piezo-electric ceramics, and ultrasonic sensors that was enabling structural health monitoring. More recently, it has been improvements in fiber optic sensors, wireless sensors and RFID tags that are enabling this monitoring. Today, it is the falling cost of these components and their combination with more recently available ones such as ionomers (a type of polymer), carbon nano-tubes, and energy harvesters. Improvements in these sensors have enabled the absolute cost of sensors and their percentage of costs in for example bridges to fall over the last 20 years to fall. These trends are expected to continue and become applicable to a broader number of structures including buildings and vehicles.
Structural Health Monitoring of Bridges Buildings and Industrial Plant with N...Polytec, Inc.
Learn about Polytec’s latest laser vibrometer, specifically designed for remote, long range vibration and deflection measurements on bridges, buildings, towers, industrial plant, high voltage insulators or indeed any surface that is inaccessible or hard to reach. The system features a very high optical sensitivity, which means that it can also be used on surfaces at distances that would otherwise require surface treatment for vibrometry measurement. The webinar will share examples showing how the RSV-150 saves time and effort when monitoring the health of structures, including the measurement of resonant frequencies and deflections of bridges subjected to traffic loading. Find out how the laser Doppler approach compares with the alternative contacting and remote sensing methods.
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
Nonlinear Viscoelastic Analysis of Laminated Composite Plates – A Multi Scale...rtme
Laminated composite plates are widely used in modern structures. Resins of composites are almost made of
polymers which show time dependent and and in some cases stress dependent behaviour. In this paper, a
laminated composite plate is analysed using a multiscale method. At first, material properties of a lamina is
obtained using an analytical micromechanical approach called simplified unit cell method (SUCM) and
then in macromechanical level, Generalized Differential Quadrature Method (GDQM) is used to analyse
laminated composite plate. Schapery's integral is used to model nonlinear viscoelastic behaviour of the
matrix. Prony series is considered to define the compliance of matrix. Micromechanical process includes
obtaining overall properties of the composite by SUCM. Both geometrical and material nonlinearity are
taken into account in order to multiscale analysis of laminated composite plate.
Comparative study of results obtained by analysis of structures using ANSYS, ...IOSR Journals
The analysis of complex structures like frames, trusses and beams is carried out using the Finite
Element Method (FEM) in software products like ANSYS and STAAD. The aim of this paper is to compare the
deformation results of simple and complex structures obtained using these products. The same structures are
also analyzed by a MATLAB program to provide a common reference for comparison. STAAD is used by civil
engineers to analyze structures like beams and columns while ANSYS is generally used by mechanical engineers
for structural analysis of machines, automobile roll cage, etc. Since both products employ the same fundamental
principle of FEM, there should be no difference in their results. Results however, prove contradictory to this for
complex structures. Since FEM is an approximate method, accuracy of the solutions cannot be a basis for their
comparison and hence, none of the varying results can be termed as better or worse. Their comparison may,
however, point to conservative results, significant digits and magnitude of difference so as to enable the analyst
to select the software best suited for the particular application of his or her structure.
Three dimensional static analysis of two dimensional functionally graded platesrtme
In this paper, static analysis of two dimensional functionally graded plates based on three dimensional
theory of elasticity is investigated. Graded finite element method has been used to solve the problem. The
effects of power law exponents on static behavior of a fully clamped 2D-FGM plate have been investigated.
The model has been compared with result of a 1D-FGM plate for different boundary conditions, and it
shows very good agreement
Three dimensional static analysis of two dimensional functionally graded platesijmech
In this paper, static analysis of two dimensional functionally graded plates based on three dimensional theory of elasticity is investigated. Graded finite element method has been used to solve the problem. The effects of power law exponents on static behavior of a fully clamped 2D-FGM plate have been investigated. The model has been compared with result of a 1D-FGM plate for different boundary conditions, and it shows very good agreement.
A Numerical Method for Modelling Discontinuous Mechanics of Asphalt MixtureIDES Editor
In order to simulate discontinuous mechanics for
asphalt mixture pavement, a new numerical scheme—
Meshfree Manifold Method is deduced in this paper by
integrating Numerical Manifold Method and Mesh-free
Method, which is not only appropriate for contact computation
but easy to eliminate the limitation of regular mesh. Some
kernel principles are discussedÿand an example is given to
prove its efficiency in simulating discontinuous deformation
of asphalt mixture.
GDQ SIMULATION FOR FLOW AND HEAT TRANSFER OF A NANOFLUID OVER A NONLINEARLY S...AEIJjournal2
This paper presents the generalized differential quadrature (GDQ) simulation for analysis of a nanofluid
over a nonlinearly stretching sheet. The obtained governing equations of flow and heat transfer are
discretized by GDQ method and then are solved by Newton-Raphson method. The effects of stretching
parameter, Brownian motion number (Nb), Thermophoresis number (Nt) and Lewis number (Le), on the
concentration distribution and temperature distribution are evaluated. The obtained results exhibit that
Analysis and Design of One Dimensional Periodic Foundations for Seismic Base ...IJERA Editor
Periodic foundationis a new type of seismic base isolation system. It is inspired by the periodic material crystal
lattice in the solid state physics. This kind of material has a unique property, which is termed as frequency band
gap that is capable of blocking incoming waves having frequencies falling within the band gap. Consequently,
seismic waves having frequencies falling within the frequency band gap are blocked by the periodic foundation.
The ability to block the seismic waveshas put this kind of foundation as a prosperous next generation of seismic
base isolators. This paper provides analytical study on the one dimensional (1D) type periodic foundations to
investigate their seismic performance. The general idea of basic theory of one dimensional (1D) periodic
foundations is first presented.Then, the parametric studies considering infinite and finite boundary conditions are
discussed. The effect of superstructure on the frequency band gap is investigated as well. Based on the analytical
study, a set of equations is proposed for the design guidelines of 1D periodic foundations for seismic base
isolation of structures.
Analysis and Design of One Dimensional Periodic Foundations for Seismic Base ...IJERA Editor
Periodic foundationis a new type of seismic base isolation system. It is inspired by the periodic material crystal
lattice in the solid state physics. This kind of material has a unique property, which is termed as frequency band
gap that is capable of blocking incoming waves having frequencies falling within the band gap. Consequently,
seismic waves having frequencies falling within the frequency band gap are blocked by the periodic foundation.
The ability to block the seismic waveshas put this kind of foundation as a prosperous next generation of seismic
base isolators. This paper provides analytical study on the one dimensional (1D) type periodic foundations to
investigate their seismic performance. The general idea of basic theory of one dimensional (1D) periodic
foundations is first presented.Then, the parametric studies considering infinite and finite boundary conditions are
discussed. The effect of superstructure on the frequency band gap is investigated as well. Based on the analytical
study, a set of equations is proposed for the design guidelines of 1D periodic foundations for seismic base
isolation of structures.
Radiation patterns account of a circular microstrip antenna loaded two annularwailGodaymi1
In this paper, theoretical study of circular microstrip antenna loaded two annular (CMSAL2AR) and calculation
of the radiation pattern using principle equivalence with moment of method formulation of electromagnetic
radiation in this these based on the bodies of revolution (BoR), which are generated by revolution a planar curve
about an axis called axis of symmetry to solving the electric fields integral equation (EFIE) and magnetic field
integral equation (MFIE). To find an unknown electric current density on the conductor surface ,and both
unknowns electric and magnetic density current on the dielectric surface which are responsible for the
generation of far fields radiation in the space for the components (Eθ ,Eφ) ,the surface currents was represented
by a set of basis functions that give the Fourier series because the body has a circular symmetry property and
then select a set of weighted functions to find a linear system by using Galerkin method which requires that the
weighted functions are equal to the complex conjugate of the current ( ) * W = J .from radiation pattern
calculated the Directive gain can be utilized to the directive gain increased to (G= 21.30 dB) when
( 0.015λ 1 = g R ) for the ratio of (Rab= 5.5), and bandwidth has been better (BW%= 19.9%) when
( 0.01λ 1 = g R ) for the ratio (Rab= 6.5) .
On the Mathematical Structure of the Fundamental Forces of NatureRamin (A.) Zahedi
The main idea of this article is based on my previous articles (references [1], [2], [3]). In this work by introducing a new mathematical approach based on the algebraic structure of integers (the domain of integers), and assuming the “discreteness” of physical quantities such as the components of the relativistic n-momentum, we derive all the mathematical laws governing the fundamental forces of nature. These obtained laws that are unique, distinct and in the form of the complex tensor equations, represent the force of gravity, the electromagnetic (including electroweak) force, and the (strong) nuclear force (and only these three kinds of forces, for all dimensions D ≥2). Each derived tensor equation contains the term of the mass m_0 (as the invariant mass of the supposed force carrier particle), as well as the term of the external current (as the external source of the force field). In some special cases, these tensor equations are turned into the wave equations that are similar to the Pauli and Dirac equations. In fact, the mathematical laws obtained in this paper, are the corrected and generalized forms of the current field equations including Maxwell equations, Yang-Mils equations and Einstein equations, as well as (in some special conditions) Pauli equation, Dirac equation, and so on. A direct proof of the absence of magnetic monopoles in nature is one of the outcomes of this research, according to the unique formulations of the laws of the fundamental forces that we have derived.
Keywords: Foundations of Physics, Ontology, Discrete Physics, Discrete Mathematics, The Fundamental Forces of Nature.
Comments: 51 Pages. Expanded version of my previous articles:
Ramin (A.) Zahedi, "Linearization Method in the Ring Theory," Bulletin of the Lebedev Physics Institute, Springer-Verlag, No. 5-6, 1997;
Ramin (A.) Zahedi, "On the Connection Between Methods of the Ring Theory and the Group Approach", Bulletin of the Lebedev Physics Institute, Springer-Verlag, No. 7-8, 1997.
PACS Classifications: 04.20.Cv, 04.50.Kd, 04.90.+e, 04.62.+v, 02.10.Hh, 02.10.Yn, 02.20.Bb, 02.90.+p, 03.50.-z, 03.65.Fd, 03.65.Pm, 03.50.Kk, 12.40.-y, 12.60.-i, 12.10.Dm, 12.10.-g.
External URL: http://arXiv.org/abs/1501.01373. (arXiv:1501.01373 [physics.gen-ph])
Copyright: CC Attribution-NonCommercial-NoDerivs 4.0 International
License URL: https://creativecommons.org/licenses/by-nc-nd/4.0/
INVERSIONOF MAGNETIC ANOMALIES DUE TO 2-D CYLINDRICAL STRUCTURES –BY AN ARTIF...ijsc
Application of Artificial Neural Network Committee Machine (ANNCM) for the inversion of magnetic
anomalies caused by a long-2D horizontal circular cylinder is presented. Although, the subsurface targets
are of arbitrary shape, they are assumed to be regular geometrical shape for convenience of mathematical
analysis. ANNCM inversion extract the parameters of the causative subsurface targets include depth to the
centre of the cylinder (Z), the inclination of magnetic vector(Ɵ)and the constant term (A)comprising the
radius(R)and the intensity of the magnetic field(I). The method of inversion is demonstrated over a
theoretical model with and without random noise in order to study the effect of noise on the technique and
then extended to real field data. It is noted that the method under discussion ensures fairly accurate results
even in the presence of noise. ANNCM analysis of vertical magnetic anomaly near Karimnagar, Telangana,
India, has shown satisfactory results in comparison with other inversion techniques that are in vogue.The
statistics of the predicted parameters relative to the measured data, show lower sum error (<9.58%) and
higher correlation coefficient (R>91%) indicating that good matching and correlation is achieved between
the measured and predicted parameters.
INVERSIONOF MAGNETIC ANOMALIES DUE TO 2-D CYLINDRICAL STRUCTURES –BY AN ARTIF...ijsc
Application of Artificial Neural Network Committee Machine (ANNCM) for the inversion of magnetic
anomalies caused by a long-2D horizontal circular cylinder is presented. Although, the subsurface targets
are of arbitrary shape, they are assumed to be regular geometrical shape for convenience of mathematical
analysis. ANNCM inversion extract the parameters of the causative subsurface targets include depth to the
centre of the cylinder (Z), the inclination of magnetic vector(Ɵ)and the constant term (A)comprising the
radius(R)and the intensity of the magnetic field(I). The method of inversion is demonstrated over a
theoretical model with and without random noise in order to study the effect of noise on the technique and
then extended to real field data. It is noted that the method under discussion ensures fairly accurate results
even in the presence of noise. ANNCM analysis of vertical magnetic anomaly near Karimnagar, Telangana,
India, has shown satisfactory results in comparison with other inversion techniques that are in vogue.The
statistics of the predicted parameters relative to the measured data, show lower sum error (<9.58%) and
higher correlation coefficient (R>91%) indicating that good matching and correlation is achieved between
the measured and predicted parameters.
Inversion of Magnetic Anomalies Due to 2-D Cylindrical Structures – By an Art...ijsc
Application of Artificial Neural Network Committee Machine (ANNCM) for the inversion of magnetic anomalies caused by a long-2D horizontal circular cylinder is presented. Although, the subsurface targets are of arbitrary shape, they are assumed to be regular geometrical shape for convenience of mathematical analysis. ANNCM inversion extract the parameters of the causative subsurface targets include depth to the centre of the cylinder (Z), the inclination of magnetic vector(Ɵ)and the constant term (A)comprising the radius(R)and the intensity of the magnetic field(I). The method of inversion is demonstrated over a theoretical model with and without random noise in order to study the effect of noise on the technique and then extended to real field data. It is noted that the method under discussion ensures fairly accurate results even in the presence of noise. ANNCM analysis of vertical magnetic anomaly near Karimnagar, Telangana, India, has shown satisfactory results in comparison with other inversion techniques that are in vogue.The statistics of the predicted parameters relative to the measured data, show lower sum error (<9.58%) and higher correlation coefficient (R>91%) indicating that good matching and correlation is achieved between the measured and predicted parameters.
The approximate bound state of the nonrelativistic Schrӧdinger equation was
obtained with the modified trigonometric scarf type potential in the framework of
asymptotic iteration method for any arbitrary angular momentum quantum number l
using a suitable approximate scheme to the centrifugal term. The effect of the screening
parameter and potential depth on the eigenvalue was studied numerically. Finally, the
scattering phase shift of the nonrelativistic Schrӧdinger equation with the potential
under consideration was calculated.
ANALYTICAL BENDING ANALYSIS OF A CIRCULAR SANDWICH PLATE UNDER DISTRIBUTED LOADijmech
In this paper, bending analysis of a circular sandwich plate under distributed load with simply supported and clamped boundary conditions is investigated. First, the governing equations of the circular sandwich plate are obtained and they are solved using the Bessel functions. Then in order to validate the correctness of analytical results, numerical finite element method is used and its results are presented in the forms of
contours and graphs. The results indicate that under distributed load, maximum deflection happens at 0.3
of outside radius, away from centre, and minimum deflection occurs at the outer edge of the circular sandwich plate. The results from analytical and numerical methods are compared and it shows that analytical method provides an acceptable accuracy.
1. NATIONAL CONFERENCE ON NEW HORIZONS IN
CIVIL ENGINEERING – NHCE 2013
April 12-13 at M.I.T, Manipal,
MODELING OF ELASTIC WAVE PROPAGATION IN PLATE
STRUCTURES USING SPECTRAL ELEMENT METHOD
Mallesh N. G.1
, Ashwin U.2
, S. Raja3
, K. Balakrishna Rao4
1, 4
Department of Civil Engineering, Manipal Institute of Technology, Manipal – 576 104
malleshnenkat@gmail.com and kb.rao@manipal.edu
2, 3
STTD, CSIR - National Aerospace Laboratories, Bangalore – 560 017
ashwin@nal.res.in and raja@nal.res.in
ABSTRACT
Modeling mid and high frequency elastic wave (>10 KHz) in thin / moderately thick elastic
plates using spectral element method has been studied. High frequency elastic waves in plates of
thickness approx. 1–2mm has a wavelength of 38 – 13 mm in a frequency range of 10 – 100
KHz. Modeling such plates excited with such small wavelength waves using Finite Element
Method leads to erroneous results in terms of time of flight and amplitude of response. Hence, in
order to accurately capture elastic wave propagation, spectral element having higher order
polynomial (6th
order) has been studied. This element has 36 nodes and can model in-plane (u, v,
w) and out-of-plane deformations (x, y). The modeled element is then simulated for wave
propagation using a unit load applied on a square plate, clamped on all the sides.
The understanding of the propagation behavior of high frequency elastic wave (Lamb waves) in
thin-walled layered structures is a very important basis of Structural Health Monitoring (SHM)
in large-scale constructions.
INTRODUCTION
The Finite Element Method (FEM) is used to solve complex problem from various fields of
physical science described by partial differential equation or integral equation. A characteristic
property of finite element method is discretization of the analyzed area into a certain number of
smaller subareas known as finite element. The stiffness and mass properties of these finite
elements are well defined, which are assembled to form the global stiffness and mass matrices.
Hence, Finite Element method is widely used to model complex physical systems, for their static
and dynamic simulations.
Spectral Element Method (SEM) is relatively new computational technique, where the element is
defined using higher order polynomials. Such polynomials are usually orthogonal Chebyshev
polynomial or very-high order Lobatto polynomial over non-uniformly spaced nodes. In SEM,
the computation error decreases exponentially as the order of approximating polynomial.
Therefore fast convergence of solution to exact solution is realized with lesser degrees of
freedom of the structure, in comparison with FEM.
The spectral plate element (higher order polynomial) was first developed by Kudela et.al. [1],
who formulated a single layered spectral plate element (five degrees of freedom) and they
studied the wave propagation patterns in orthotropic plate structure. In the present work, a
layered spectral plate element with 36 nodes has been formulated. The displacement and shape
of the element is approximated using Gauss-Lobatto-Legendre polynomial, which defines the
nodes to be non-uniformly distributed within the element. This non-uniform distribution of the
2. NATIONAL CONFERENCE ON NEW HORIZONS IN
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April 12-13 at M.I.T, Manipal,
nodes makes the mass matrix of the element diagonal. Since, the wave propagation is
numerically solved using explicit solvers (Time integration using central difference method),
inverse of diagonal mass matrix becomes very simple to solve, making the computation very
fast. The plate has been modeled using first order shear deformation theory, and the ABD matrix
is appropriately constructed. To demonstrate the spectral element simulation of wave
propagation, a square plate of length to thickness ratio of 266 has been modeled. The plate
clamped from all sides and excited at the centre using amplitude modulated signal.
BACKGROUND STUDIES
Mindlin-Reissner theory
The element is formulated using Mindlin-Reissner theory of plates, which takes into account the
shear deformation. The kinematic relations, constitutive relation and strain – displacement
relations are given in equations 1-2, equation 3 and equations 4-8, respectively.
0 yu u z (1)
0 xv v z (2)
11 12 13
21 22 23
31 32 33
44
55
66
0 0 0
0 0 0
0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
x x
x y
x z
yz yz
zx zx
xy xy
Q Q Q
Q Q Q
Q Q Q
Q
Q
Q
(3)
00
y
x x x
uu
z zk
x x x
(4)
00
x
y y y
vv
z zk
y y y
(5)
00 0
y x
xy xy xy
u vu v
z z zk
y x y x y x
(6)
0
xz y
ww u
x z x
(7)
0
yz x
ww v
y z y
(8)
ABD Matrix
The layer-wise material stiffness matrices and the force and moment resultants for plane stress
condition are shown in equation 11 and equations 9-10, respectively.
3. NATIONAL CONFERENCE ON NEW HORIZONS IN
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1 1
_ _ _ _ _ _
0
11 12 16 11 12 16
_ _ _ _ _ _
0
12 22 26 12 22 26
_ _ _ 0 _ _ _
1 1
16 26 66 16 26 66
k k
k k
n n
xh hx
y xh h
k k
xy xy
x
y
xy
Q Q Q Q Q Q
N
N Q Q Q dz Q Q Q zdz
N
Q Q Q Q Q Q
(9)
1 1
_ _ _ _ _ _
0
11 12 16 11 12 16
_ _ _ _ _ _
0 2
12 22 26 12 22 26
_ _ _ 0 _ _ _1 1
16 26 66 16 26 66
k k
k k
n nxx h h
h hy x
k k
xy xy
x
y
xy
Q Q Q Q Q Q
M
M Q Q Q zdz Q Q Q z dz
M
Q Q Q Q Q Q
(10)
4 2 2 4
11 11 12 66 22cos 2( 2 )sin cos sin Q Q Q Q Q
4 2 2 4
22 11 12 66 22sin 2( 2 )sin cos cos Q Q Q Q Q
3 3
16 11 12 66 12 22 66( 2 )sin cos ( 2 )sin cos Q Q Q Q Q Q Q
3 3
26 11 12 66 12 22 66( 2 )sin cos ( 2 )sin cos Q Q Q Q Q Q Q
2 2 4 4
66 11 12 12 66 66( 2 2 )sin cos (sin cos ) Q Q Q Q Q Q
2 2
44 44 55cos sin Q Q Q
45 55 44( )sin cos Q Q Q
2 2
55 55 44cos sin Q Q Q (11)
SPECTRAL ELEMENT FORMULATION
Interpolation function and Gaussian Quadrature
The Legendre polynomial of nth order is defined as,
21
( ) ( 1) 0,1,2...
2 !
n
n
n n n
d
P where n
n d
(12)
In the current formulation 5th
order Legendre polynomial is chosen, Hence 36 nodes can be
specified in the local coordinate system of the element , (shown in Figure 1)
,
,
( ) , 1,2......6,
1 2 1 2 1 2 1 2
1, , , , ,1
3 3 3 33 7 3 7 3 7 3 7
m n
m n
m n
(13)
The weight Gaussian weight are given as,
4. NATIONAL CONFERENCE ON NEW HORIZONS IN
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April 12-13 at M.I.T, Manipal,
, 0.0667 0.3785 0.5549 0.5549 0.3785 0.0667m nw
Figure 1 – 36 noded spectral finite element
The interpolation function, when applied unit displacement at different nodes are shown in
Figures 2- 5.
Figure 2, Nodal point 1 (Refer Figure 1) Figure 3, Nodal point 11 (Refer Figure 1)
Figure 4, Nodal point 22 (Refer Figure 1) Figure 5, Nodal point 34 (Refer Figure 1)
Geometry and Displacement model (Iso-parametric)
Shape functions are formed on the specified nodes to approximate the geometry of the element in
the global coordinate system and also to approximate the displacements within the element
1 2 3 4 5 6
31 32 33 34 35 36
7 8 9 10 11 12
25 26 27 28 29 30
19 20 21 22 23 24
13 14 15 16 17 18
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The geometric equations using Lobatto Lagrangian interpolation function can be written as,
36 6 6
, ,
1 1 1
( ) ( ) ( ) ( )
m n k m n k m n mn
k m n
x N x N N x (14)
36 6 6
, ,
1 1 1
( ) ( ) ( ) ( )
m n k m n k m n mn
k m n
y N y N N y (15)
Where )(mN and )(mN are one dimension shape functions, obtained from equation 12, which
is written independently for the two coordinates.
The displacement equations using Lobatto Lagrangian interpolation function is written as,
36 6 6
, ,
1 1 1
( ) ( ) ( ) ( )
m n k m n k m n mn
k m n
u N u N N u (16)
36 6 6
, ,
1 1 1
( ) ( ) ( ) ( )
m n k m n k m n mn
k m n
v N v N N v (17)
36 6 6
, ,
1 1 1
( ) ( ) ( ) ( )
m n k m n k m n mn
k m n
w N w N N w (18)
36 6 6
, ,
1 1 1
( ) ( ) ( ) ( )
x m n k m n xk m n xmn
k m n
N N N (19)
36 6 6
, ,
1 1 1
( ) ( ) ( ) ( )
y m n k m n yk m n ymn
k m n
N N N (20)
Strain – Displacement Relation
The strain – displacement relation is obtained by substituting equations 16-20 in equations 4-8
as,
0
0
0
36 36
1 1
0 0 0 0
0 0 0 0
0 0 0
0 0 0 0
0 0 0 0
0 0 0
0 0 0
0 0 0
i
i
i ix
y
ixy
x
i i
iy i i x
xy
ys
i ixy
s
xy
i
i
i
i
N
x
N
y
N N
y x
uN
v
x wB q N
y
N N
x y
N
N
x
N
N
y
i
(21)
6. NATIONAL CONFERENCE ON NEW HORIZONS IN
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Element Stiffness and Mass Matrix
The element stiffness is then computed from equations 21 and 10 as,
T
AK B ABD B dxdy (22)
Similarly, the mass matrix is written as,
T
AM N N dxdy (23)
Where,
0 0 0 0
0 0 0 0
0 0 0 0 , 1 36
0 0 0 0
0 0 0 0
i
i
i
i
i i
N
N
N N where i to
N
N
The element stiffness and mass matrix in equations 22-23 is assembled to obtain the global
stiffness and mass matrix.
Central Difference Method
The central difference method computes the time integration on elastic wave propagation and the
displacement in the next time step ( x t t ) is computed using the displacement information of
the current ( x t ) and previous ( x t t ) time steps as follows,
2 2
2
2 ( )1
( ) ( ) ( ) ( )
2
2
g g g
g
g g
M x t M C
x t t f t K x t x t t
M C t t t
t t
(24)
Where, gK , gM , and gC are the global stiffness, mass and damping matrices. In the present
work, the damping has been taken as zero, which makes the solution of equation 24, very simple
and computationally very fast.
RESULTS AND DISCUSSION
To demonstrate the simulation using spectral element, a square plate of dimension 400 × 400
mm2
and 1.5mm has been modeled. The plate is clamped on all edges and excited with a point
load of 1N at the centre. The excitation signal 3.5 cycle amplitude modulated. The simulation of
the wave propagation at different propagation time is presented. Figure 6 shows the excitation
point of the wave, Figure 7 the wave propagation through the plate, Figure 8 shows the start of
wave reflection at the plate boundary, Figure 9 shows the reflected wave from the plate boundary
and Figures 10 and 11 shows the wave interacting reflecting the different boundaries of the plate.
7. NATIONAL CONFERENCE ON NEW HORIZONS IN
CIVIL ENGINEERING – NHCE 2013
April 12-13 at M.I.T, Manipal,
Figure 6, Wave propagation (0.4 µs) Figure 7, Wave propagation (0.266 µs)
Figure 8, Wave propagation (0.2 µs) Figure 9, Wave propagation (0.16 µs)
Figure 10, Wave propagation (0.133 µs) Figure 11, Wave propagation (0.1143 µs)
CONCLUSIONS
The forumulated element is very efficient in simulating elastic wave propagation (lamb wave)
and is computationally very efficient in comparison to finite element method. The element needs
to be benchmarked by comparsing the group velocity with that esimated theoretically from the
dispersion curves. Further, we also intend to extend the procedure to model piezoelectric actuator
and sensor.
8. NATIONAL CONFERENCE ON NEW HORIZONS IN
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REFERENCES
[1] Pawel Kudela, Arkadiusz Zak, Marek Krawczuk, Wieslaw Ostachowicz, Modeling of wave
propagation in composite plates using the time domain spectral element method, Journal of
sound and vibration 302(2007) 728-745.
[2] C. S. Krishnamoorthy, Finite Element Analysis, Tata McGraw Hill Education private
Limited, New Delhi, 2010
[3] Wieslaw Ostachowicz, Pawel Kudela, Marek Krawczuk, Arkadiusz Zak, Guided waves in
Structures for SHM, Wiley, United Kingdom, 2012.
[4] Autar K. Kaw, Mechanics of Composite Material, Taylor & Francis, New York, 2006
[5] Giora Maymon, Structural Dynamics and Probabilistic Analyses for Engineer, Elsevier,
Jordan Hill, 2008
[6] J.N Reddy, Mechanics of Laminated Composite Plates, CRC press, New York, 1997