This document presents a model for analyzing the vibration and stochastic wave response of a tension leg platform (TLP). It describes:
1) Modeling the TLP as a compliant structure with a mass connected to a torsional spring, accounting for viscous damping from seawater.
2) Deriving the input and output spectral densities by taking the Fourier transform of the autocorrelation function of the random input force and multiplying it by the transfer function obtained from the equation of motion.
3) The resulting output spectral density plot shows spikes at frequencies where there is maximum energy in the system, indicating the variance is concentrated at those frequencies.
This document provides an overview of Module 1: Oscillations and Waves. It covers the following topics:
1. Free oscillations, including the definition and characteristics of simple harmonic motion, the differential equation of motion, mechanical oscillations using a mass-spring system, and complex notation.
2. Damped and forced oscillations, including the theory of damped oscillations involving overdamping, critical damping, and underdamping. It also discusses forced oscillations and resonance.
3. Shock waves, including definitions of Mach number, properties and laws governing shock waves, and applications involving shock tube experiments.
4. The document concludes with references on oscillations, vibrations, and waves from various textbooks and journals
The Effect of Bottom Sediment Transport on Wave Set-Upijceronline
In this paper we augment the wave-averaged mean field equations commonly used to describe wave set-up and wave-induced mean currents in the near-shore zone, with an empirical sediment flux law depending only on the wave-induced mean current and mean total depth. This model allows the bottom to evolve slowly in time, and is used to examine how sediment transport affects wave set-up in the surf zone. We show that the mean bottom depth in the surf zone evolves according to a simple wave equation, whose solution predicts that the mean bottom depth decreases and the beach is replenished. Further, we show that if the sediment flux law also allows for a diffusive dependence on the beach slope then the simple wave equation is replaced by a nonlinear diffusion equation which allows a steady-state solution, the equilibrium beach profile
International Journal of Computational Engineering Research(IJCER)ijceronline
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.
Design and characterization of a nano-Newton resolution thrust stand - RSIJignesh Soni, PhD
The document describes the design and calibration of a thrust stand capable of measuring nano-Newton forces. Key points:
- The thrust stand uses a torsion balance design with a cross-beam acting as the torsion spring. An eddy current damper provides damping without contact.
- Calibration is done using three methods and compared to choose the optimal one. Natural frequency measurements, moment of inertia calculations, and controlled deflections are used.
- Testing shows the thrust stand can resolve forces as low as 1.3 μN with 20% uncertainty. This resolution is suitable for measuring small thrusters for nanosatellites.
Introduction to oscillations and simple harmonic motionMichael Marty
Physics presentation about Simple Harmonic Motion of Hooke's Law springs and pendulums with derivation of formulas and connections to Uniform Circular Motion.
References include links to illustrative youtube clips and other powerpoints that contributed to this peresentation.
This document discusses simple harmonic motion (SHM). SHM occurs when an object experiences a restoring force proportional to its displacement from equilibrium. This results in sinusoidal oscillations described by x(t) = Acos(ωt + φ), where A is amplitude, ω is angular frequency, and φ is the phase. SHM includes examples like a mass on a spring and a simple pendulum. The relationships between displacement, velocity, acceleration, period, frequency, and energy in SHM systems are explored.
This document provides an outline on the topic of harmonic motion in physics. It discusses key concepts such as Hooke's law, elastic potential energy, simple harmonic motion, the period and frequency of oscillation, and using a simple pendulum as an example of simple harmonic motion. The document defines important terms and provides examples to illustrate harmonic motion concepts.
This chapter discusses simple harmonic motion (SHM). SHM is defined as periodic motion where the acceleration is directly proportional to and opposite of the displacement from equilibrium. The key equations of SHM are introduced, including the displacement equation x = A sin(ωt + φ) and equations for velocity, acceleration, kinetic energy, and potential energy using angular frequency ω. Examples of SHM include a simple pendulum and spring oscillations. Exercises are provided to apply the kinematic equations of SHM.
This document provides an overview of Module 1: Oscillations and Waves. It covers the following topics:
1. Free oscillations, including the definition and characteristics of simple harmonic motion, the differential equation of motion, mechanical oscillations using a mass-spring system, and complex notation.
2. Damped and forced oscillations, including the theory of damped oscillations involving overdamping, critical damping, and underdamping. It also discusses forced oscillations and resonance.
3. Shock waves, including definitions of Mach number, properties and laws governing shock waves, and applications involving shock tube experiments.
4. The document concludes with references on oscillations, vibrations, and waves from various textbooks and journals
The Effect of Bottom Sediment Transport on Wave Set-Upijceronline
In this paper we augment the wave-averaged mean field equations commonly used to describe wave set-up and wave-induced mean currents in the near-shore zone, with an empirical sediment flux law depending only on the wave-induced mean current and mean total depth. This model allows the bottom to evolve slowly in time, and is used to examine how sediment transport affects wave set-up in the surf zone. We show that the mean bottom depth in the surf zone evolves according to a simple wave equation, whose solution predicts that the mean bottom depth decreases and the beach is replenished. Further, we show that if the sediment flux law also allows for a diffusive dependence on the beach slope then the simple wave equation is replaced by a nonlinear diffusion equation which allows a steady-state solution, the equilibrium beach profile
International Journal of Computational Engineering Research(IJCER)ijceronline
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.
Design and characterization of a nano-Newton resolution thrust stand - RSIJignesh Soni, PhD
The document describes the design and calibration of a thrust stand capable of measuring nano-Newton forces. Key points:
- The thrust stand uses a torsion balance design with a cross-beam acting as the torsion spring. An eddy current damper provides damping without contact.
- Calibration is done using three methods and compared to choose the optimal one. Natural frequency measurements, moment of inertia calculations, and controlled deflections are used.
- Testing shows the thrust stand can resolve forces as low as 1.3 μN with 20% uncertainty. This resolution is suitable for measuring small thrusters for nanosatellites.
Introduction to oscillations and simple harmonic motionMichael Marty
Physics presentation about Simple Harmonic Motion of Hooke's Law springs and pendulums with derivation of formulas and connections to Uniform Circular Motion.
References include links to illustrative youtube clips and other powerpoints that contributed to this peresentation.
This document discusses simple harmonic motion (SHM). SHM occurs when an object experiences a restoring force proportional to its displacement from equilibrium. This results in sinusoidal oscillations described by x(t) = Acos(ωt + φ), where A is amplitude, ω is angular frequency, and φ is the phase. SHM includes examples like a mass on a spring and a simple pendulum. The relationships between displacement, velocity, acceleration, period, frequency, and energy in SHM systems are explored.
This document provides an outline on the topic of harmonic motion in physics. It discusses key concepts such as Hooke's law, elastic potential energy, simple harmonic motion, the period and frequency of oscillation, and using a simple pendulum as an example of simple harmonic motion. The document defines important terms and provides examples to illustrate harmonic motion concepts.
This chapter discusses simple harmonic motion (SHM). SHM is defined as periodic motion where the acceleration is directly proportional to and opposite of the displacement from equilibrium. The key equations of SHM are introduced, including the displacement equation x = A sin(ωt + φ) and equations for velocity, acceleration, kinetic energy, and potential energy using angular frequency ω. Examples of SHM include a simple pendulum and spring oscillations. Exercises are provided to apply the kinematic equations of SHM.
This document discusses oscillations and wave motion. It begins by introducing mechanical vibrations and simple harmonic motion. It then covers damped and driven oscillations, as well as different oscillating systems like springs, pendulums, and driven oscillations. The document goes on to discuss traveling waves, the wave equation, periodic waves on strings and in electromagnetic fields. It also covers waves in three dimensions, reflection, refraction, diffraction, and interference of waves. Key concepts covered include amplitude, frequency, period, angular frequency, energy of oscillating systems, and resonance.
International Journal of Engineering and Science Invention (IJESI)inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
This document discusses simple harmonic motion (SHM), which refers to the periodic back-and-forth motion of an object attached to a spring or pendulum. It defines SHM as motion produced by a restoring force proportional to displacement and in the opposite direction. The key conditions for SHM are described, including that the maximum displacement from equilibrium is the amplitude. Equations show that the frequency and period of SHM depend only on the spring constant and mass. Graphs illustrate the variation in displacement, velocity, and acceleration over time for SHM. The document also discusses the conservation of energy for SHM systems, where potential and kinetic energy periodically convert between each other during the oscillation.
1. This document discusses key concepts related to oscillations and waves including: simple harmonic motion (SHM), parameters that describe SHM like amplitude, period, frequency, phase, and the relationships between displacement, velocity, and acceleration in SHM.
2. Examples of SHM include a mass on a spring and a simple pendulum. The frequency and period of oscillations can be determined from the properties of the object and spring/pendulum.
3. Forced oscillations and resonance are explored where a driving force can excite the natural frequency of an object, causing large oscillations. This can be useful or destructive depending on the situation.
This Unit is rely on introduction to Simple Harmonic Motion. the contents was prepared using the Curriculum of NTA level 4 at Mineral Resources Institute- Dodoma.
The document discusses simple harmonic motion (SHM), where a particle moves back and forth such that its acceleration is directly proportional to its distance from a fixed point. SHM has the properties that the particle's velocity is zero at the amplitude of its oscillation, and it travels between the points of -a and +a on its axis. Examples are given of particles moving according to SHM equations, and exercises are provided to practice determining SHM, periods of motion, and maximum values.
Simple harmonic motion (SHM) refers to the periodic oscillatory motion of an object where the restoring force is directly proportional to the displacement of the object from its equilibrium position. There are two types of SHM: linear SHM such as oscillations of a spring or pendulum, and angular SHM such as a torsional pendulum. The period of SHM is the time required for one complete oscillation, while the frequency is the number of oscillations that occur per second. For a spring with spring constant k and mass m, the period is 2π√(m/k). For a simple pendulum of length l, the period is 2π√(l/g). SHM can be described by equations
Mechanical wave descriptions for planets and asteroid fields: kinematic model...Premier Publishers
Models with wave dynamics and oscillations in the solar system are presented. A solitonial solution (Korteweg-de Vries), for a density field, is related to the formations of planets. A new nonlinear equation for a solitonial, will be derived, and denoted ‘J-T equation’. The linearized version has solutions, which are small vibrations with eigen frequency proportional to the parameters describing the solitonial wave, around a constant level, which is 2/3 of the maximum solitonial density. The location and orbital motion of Mercury and Venus are compared with wave dynamics. The tidal effect for Earth is analysed in terms of dynamics. Related phenomena for other planetary objects are discussed in conjunction with assuming a Roche limit.
This document provides a table of contents for a document on aerodynamics. It discusses various topics related to aerodynamics including mathematical notations, basic laws of fluid dynamics, boundary conditions, airfoil design methods, compressible flow, shock waves, and linearized flow equations. Specifically, it summarizes the conical flow method and singularity distribution method for obtaining the theoretical solution for pressure distribution on a finite span wing in supersonic flow. The conical flow method assumes the potential and other flow properties are constant along rays through a common vertex, modeling conical flow patterns seen in supersonic flows.
Aerodynamics Part II of 3 describes aerodynamics of bodies in supersonic flight.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://www.solohermelin.com.
The document summarizes a presentation on Hořava gravity, a recent theory in theoretical physics that aims to develop a quantum field theory of gravity. It breaks Lorentz invariance at ultra-high energies while retaining it at low energies. The theory has generated over 500 scientific articles since 2009. The presentation gives an overview of Hořava gravity and its key ideas, such as abandoning Lorentz invariance as fundamental and attempting to recover an approximate low-energy Lorentz invariance. It also discusses how the theory provides a physical regulator for quantum field theories while keeping Feynman diagrams finite.
1) Simple harmonic motion is the motion of an object where the acceleration is directly proportional to the displacement from the equilibrium position and directed towards the equilibrium.
2) It can be modeled as circular motion where the acceleration towards the center is proportional to the displacement from the center.
3) Simple harmonic oscillators include spring-mass systems and pendulums, where the restoring force is proportional to the displacement.
Hsc physics revision for oscillation and elasticitynitin oke
This document contains questions that may be asked about the topic of oscillation. It includes questions ranging from 1 to 4 marks testing a variety of concepts. Some of the key concepts that could be assessed include: defining terms related to simple harmonic motion such as period, amplitude, phase; deriving expressions for kinetic energy, potential energy, and total energy of a particle in SHM; representing displacement, velocity and acceleration graphs for SHM; obtaining differential equations of motion for various oscillatory systems; and analyzing composition of two SHMs. The document also provides important formulas that may be used to answer oscillation questions.
Periodic motion repeats at regular time intervals. Examples include planetary orbits and clock hands. Oscillation involves to-and-fro motion about a mean position, like a pendulum swing. It is always periodic but periodic motion need not involve oscillation. The time for one full cycle is the period (T). Frequency (ν) is the number of cycles per second. Angular frequency (ω) relates frequency and period. Displacement variables describe the changing quantity in oscillations, like position or angle. Simple harmonic motion involves a restoring force proportional to displacement towards the equilibrium point, like a spring. It can be modeled by sine and cosine functions and includes oscillations of springs and pendulums.
This document defines key terms and equations related to simple harmonic motion (SHM). It discusses oscillating systems that vibrate back and forth around an equilibrium point, like a mass on a spring or pendulum. The key parameters of SHM systems are defined, including amplitude, wavelength, period, frequency, displacement, velocity, acceleration. Equations are presented that relate the displacement, velocity, acceleration as sinusoidal functions of time. The concepts of kinetic, potential and total energy are also explained for oscillating systems undergoing SHM.
A simple pendulum consists of a weight suspended from a pivot that is free to swing back and forth. When displaced from its resting position, gravity causes the pendulum to accelerate back towards equilibrium in an oscillating motion. The time for one full cycle from left swing to right swing is called the period. The period depends on the length of the pendulum and also slightly on the amplitude or width of the swing.
This document discusses different methods for providing lateral load resistance in structures, including structural modifications, aerodynamic modifications, base isolation, and damping sources. It focuses on tuned liquid dampers, which use sloshing liquid in a container to dissipate vibrational energy. Tuned liquid dampers can be tuned to the natural frequency of a structure by adjusting their dimensions and work through sloshing of liquid in rectangular or cylindrical containers, usually filled with water. They provide effective damping against wind and earthquake vibrations at low cost and maintenance.
Tuned mass damper (TMD) adalah alat kontrol yang terdiri dari massa, pegas, dan peredam yang dipasang pada struktur utama untuk mengurangi getaran akibat beban angin atau gempa. TMD dipasang pada berbagai struktur seperti gedung tinggi, menara, jembatan, dan lainnya. Prinsipnya adalah dengan mengatur frekuensi getaran TMD agar sama dengan frekuensi getaran struktur utama sehingga dapat mengur
A mass damper is a vibration absorber able to attenuate the vibrations of a structure or a machinery. By a mass damper it's possible to increase the global damping of the system without the necessity to modify the mechanical structure.
Pendulum Lap investigating the relationship between the length of the pendlum string and the time needed for the oscillations
Score archieved: 5/6 in the DCP section.
This document discusses oscillations and wave motion. It begins by introducing mechanical vibrations and simple harmonic motion. It then covers damped and driven oscillations, as well as different oscillating systems like springs, pendulums, and driven oscillations. The document goes on to discuss traveling waves, the wave equation, periodic waves on strings and in electromagnetic fields. It also covers waves in three dimensions, reflection, refraction, diffraction, and interference of waves. Key concepts covered include amplitude, frequency, period, angular frequency, energy of oscillating systems, and resonance.
International Journal of Engineering and Science Invention (IJESI)inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
This document discusses simple harmonic motion (SHM), which refers to the periodic back-and-forth motion of an object attached to a spring or pendulum. It defines SHM as motion produced by a restoring force proportional to displacement and in the opposite direction. The key conditions for SHM are described, including that the maximum displacement from equilibrium is the amplitude. Equations show that the frequency and period of SHM depend only on the spring constant and mass. Graphs illustrate the variation in displacement, velocity, and acceleration over time for SHM. The document also discusses the conservation of energy for SHM systems, where potential and kinetic energy periodically convert between each other during the oscillation.
1. This document discusses key concepts related to oscillations and waves including: simple harmonic motion (SHM), parameters that describe SHM like amplitude, period, frequency, phase, and the relationships between displacement, velocity, and acceleration in SHM.
2. Examples of SHM include a mass on a spring and a simple pendulum. The frequency and period of oscillations can be determined from the properties of the object and spring/pendulum.
3. Forced oscillations and resonance are explored where a driving force can excite the natural frequency of an object, causing large oscillations. This can be useful or destructive depending on the situation.
This Unit is rely on introduction to Simple Harmonic Motion. the contents was prepared using the Curriculum of NTA level 4 at Mineral Resources Institute- Dodoma.
The document discusses simple harmonic motion (SHM), where a particle moves back and forth such that its acceleration is directly proportional to its distance from a fixed point. SHM has the properties that the particle's velocity is zero at the amplitude of its oscillation, and it travels between the points of -a and +a on its axis. Examples are given of particles moving according to SHM equations, and exercises are provided to practice determining SHM, periods of motion, and maximum values.
Simple harmonic motion (SHM) refers to the periodic oscillatory motion of an object where the restoring force is directly proportional to the displacement of the object from its equilibrium position. There are two types of SHM: linear SHM such as oscillations of a spring or pendulum, and angular SHM such as a torsional pendulum. The period of SHM is the time required for one complete oscillation, while the frequency is the number of oscillations that occur per second. For a spring with spring constant k and mass m, the period is 2π√(m/k). For a simple pendulum of length l, the period is 2π√(l/g). SHM can be described by equations
Mechanical wave descriptions for planets and asteroid fields: kinematic model...Premier Publishers
Models with wave dynamics and oscillations in the solar system are presented. A solitonial solution (Korteweg-de Vries), for a density field, is related to the formations of planets. A new nonlinear equation for a solitonial, will be derived, and denoted ‘J-T equation’. The linearized version has solutions, which are small vibrations with eigen frequency proportional to the parameters describing the solitonial wave, around a constant level, which is 2/3 of the maximum solitonial density. The location and orbital motion of Mercury and Venus are compared with wave dynamics. The tidal effect for Earth is analysed in terms of dynamics. Related phenomena for other planetary objects are discussed in conjunction with assuming a Roche limit.
This document provides a table of contents for a document on aerodynamics. It discusses various topics related to aerodynamics including mathematical notations, basic laws of fluid dynamics, boundary conditions, airfoil design methods, compressible flow, shock waves, and linearized flow equations. Specifically, it summarizes the conical flow method and singularity distribution method for obtaining the theoretical solution for pressure distribution on a finite span wing in supersonic flow. The conical flow method assumes the potential and other flow properties are constant along rays through a common vertex, modeling conical flow patterns seen in supersonic flows.
Aerodynamics Part II of 3 describes aerodynamics of bodies in supersonic flight.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://www.solohermelin.com.
The document summarizes a presentation on Hořava gravity, a recent theory in theoretical physics that aims to develop a quantum field theory of gravity. It breaks Lorentz invariance at ultra-high energies while retaining it at low energies. The theory has generated over 500 scientific articles since 2009. The presentation gives an overview of Hořava gravity and its key ideas, such as abandoning Lorentz invariance as fundamental and attempting to recover an approximate low-energy Lorentz invariance. It also discusses how the theory provides a physical regulator for quantum field theories while keeping Feynman diagrams finite.
1) Simple harmonic motion is the motion of an object where the acceleration is directly proportional to the displacement from the equilibrium position and directed towards the equilibrium.
2) It can be modeled as circular motion where the acceleration towards the center is proportional to the displacement from the center.
3) Simple harmonic oscillators include spring-mass systems and pendulums, where the restoring force is proportional to the displacement.
Hsc physics revision for oscillation and elasticitynitin oke
This document contains questions that may be asked about the topic of oscillation. It includes questions ranging from 1 to 4 marks testing a variety of concepts. Some of the key concepts that could be assessed include: defining terms related to simple harmonic motion such as period, amplitude, phase; deriving expressions for kinetic energy, potential energy, and total energy of a particle in SHM; representing displacement, velocity and acceleration graphs for SHM; obtaining differential equations of motion for various oscillatory systems; and analyzing composition of two SHMs. The document also provides important formulas that may be used to answer oscillation questions.
Periodic motion repeats at regular time intervals. Examples include planetary orbits and clock hands. Oscillation involves to-and-fro motion about a mean position, like a pendulum swing. It is always periodic but periodic motion need not involve oscillation. The time for one full cycle is the period (T). Frequency (ν) is the number of cycles per second. Angular frequency (ω) relates frequency and period. Displacement variables describe the changing quantity in oscillations, like position or angle. Simple harmonic motion involves a restoring force proportional to displacement towards the equilibrium point, like a spring. It can be modeled by sine and cosine functions and includes oscillations of springs and pendulums.
This document defines key terms and equations related to simple harmonic motion (SHM). It discusses oscillating systems that vibrate back and forth around an equilibrium point, like a mass on a spring or pendulum. The key parameters of SHM systems are defined, including amplitude, wavelength, period, frequency, displacement, velocity, acceleration. Equations are presented that relate the displacement, velocity, acceleration as sinusoidal functions of time. The concepts of kinetic, potential and total energy are also explained for oscillating systems undergoing SHM.
A simple pendulum consists of a weight suspended from a pivot that is free to swing back and forth. When displaced from its resting position, gravity causes the pendulum to accelerate back towards equilibrium in an oscillating motion. The time for one full cycle from left swing to right swing is called the period. The period depends on the length of the pendulum and also slightly on the amplitude or width of the swing.
This document discusses different methods for providing lateral load resistance in structures, including structural modifications, aerodynamic modifications, base isolation, and damping sources. It focuses on tuned liquid dampers, which use sloshing liquid in a container to dissipate vibrational energy. Tuned liquid dampers can be tuned to the natural frequency of a structure by adjusting their dimensions and work through sloshing of liquid in rectangular or cylindrical containers, usually filled with water. They provide effective damping against wind and earthquake vibrations at low cost and maintenance.
Tuned mass damper (TMD) adalah alat kontrol yang terdiri dari massa, pegas, dan peredam yang dipasang pada struktur utama untuk mengurangi getaran akibat beban angin atau gempa. TMD dipasang pada berbagai struktur seperti gedung tinggi, menara, jembatan, dan lainnya. Prinsipnya adalah dengan mengatur frekuensi getaran TMD agar sama dengan frekuensi getaran struktur utama sehingga dapat mengur
A mass damper is a vibration absorber able to attenuate the vibrations of a structure or a machinery. By a mass damper it's possible to increase the global damping of the system without the necessity to modify the mechanical structure.
Pendulum Lap investigating the relationship between the length of the pendlum string and the time needed for the oscillations
Score archieved: 5/6 in the DCP section.
A tuned mass damper is a device that reduces unwanted vibrations in structures by absorbing and dissipating the structure's energy. It consists of a mass attached to the structure with springs and dampers. The mass is tuned to the fundamental frequency of the structure so that it vibrates out of phase, canceling out the structural vibrations. Tuned mass dampers are commonly used in tall buildings, bridges, and other structures to reduce motion caused by wind or earthquakes and improve occupant comfort and structural integrity. They provide effective vibration control without an external power source, though proper tuning is required and a large mass may be needed.
Taipei 101 is a 508-meter, 101-story skyscraper in Taipei, Taiwan. It features a deep foundation of 380 concrete piles sunk 80 meters into the soft clay soil to withstand earthquakes and typhoons. The building's tuned mass damper, a 736-ton steel sphere suspended from cables, helps counteract wind forces. Construction from 1999-2004 overcame challenges from Taiwan's seismic and weather conditions through a flexible supercolumn system and the world's largest damper.
Taipei 101 is a landmark 101-story skyscraper in Taipei, Taiwan. It was the world's tallest building from 2004 to 2010. Some key points:
- Taipei 101 was designed to withstand typhoons and earthquakes and has structural systems like outrigger trusses, belt trusses, and a 660-tonne tuned mass damper to absorb vibrations.
- At 508 meters tall with 101 floors above ground, it held several height records for buildings until surpassed by Burj Khalifa.
- The building's structural design uses steel and concrete columns, including eight large "mega-columns", to support its height and resist lateral forces.
- Taipei
This document summarizes information about vibration analysis and damping in structures. It discusses causes and effects of structural vibration, methods for reducing vibration, and analyzing structural vibration through modeling and solving equations of motion. Specific topics covered include free and forced vibration of structures with one degree of freedom, damping methods like viscous, dry friction and hysteretic, vibration isolation, shock excitation, and wind-excited oscillation. Sources of damping in structures and methods for adding damping like dampers and absorbers are also summarized.
Offshore platforms are large structures located at sea that house crews and machinery used for exploring and producing natural resources like fossil fuels from under the ocean bed. There are various types of offshore platforms including fixed platforms, compliant towers, jack-up platforms, semi-submersible platforms, drillships, tension-leg platforms, SPAR platforms, and unmanned installations. Over 6,500 offshore oil and gas platforms are located around the world, with the largest numbers in the Gulf of Mexico, Asia, and Europe. Platforms can be either fixed to the seabed or floating, and are used to extract resources from shallow to very deep waters.
A Tension Leg Platform (TLP) is a floating structure connected via pre-tensioned tendons to a fixed foundation underneath. The tendons restrain motion in heave, roll, and pitch while allowing movement in surge, sway, and yaw. A TLP is used for drilling, production, and export of hydrocarbons from offshore oil fields. It must be designed to operate safely in different conditions and to allow relocation if needed. Requirements and references are provided for riser systems, mooring if used, and stability calculations.
This document provides an introduction to mechanical vibrations. It discusses fundamentals such as single and multi degree of freedom systems, free and forced vibrations, harmonic and random vibrations. Examples of vibratory systems include vehicles, rotating machinery, musical instruments. Excessive vibrations can cause issues like noise, fatigue failure. The Tacoma Narrows bridge collapse and Millennium bridge vibrations are discussed. Harmonic motion and its characteristics such as amplitude, period, frequency, and phase are also introduced.
The slam induced loads on two-dimensional bodies have been studied by applying an explicit
finite element code which is based on a multi-material arbitrary Lagrangian-Eulerian
formulation and penalty coupling method. This work focuses on the assessment of total
vertical slamming force, pressure distributions at different time instances and pressure
histories on the wetted surfaces of typical rigid bodies. Meanwhile, the simulation technique
involved in the two-dimensional slamming problem is discussed through related parameter
study.
The document summarizes principles for capturing energy from ocean waves through oscillating water column devices or floating bodies. It discusses that:
1) To absorb wave energy, a device must displace water in an oscillating manner that is in the correct phase with the incoming waves to destructively interfere and cancel them out.
2) For maximum energy capture, a device needs to oscillate at the optimum amplitude and phase for the incoming wave conditions. The phase should match the natural frequency of the device or be controlled to do so.
3) Phase control can be achieved through "latching" where a small amount of energy is returned to the sea during each cycle to better match the phase of the incoming waves
This document discusses mechanical vibrations and introduces several key concepts:
- Mass or inertia elements represent the masses in a mathematical model of a vibrating system. Springs represent elastic elements.
- Multiple masses can be combined into an equivalent single mass to simplify analysis. This is done by equating kinetic energies.
- Damping occurs through various mechanisms that dissipate vibrational energy as heat or sound. These include viscous damping from fluid resistance, dry friction or Coulomb damping, and material or hysteretic damping within deforming solids.
This document presents a method for stochastic hydroelastic analysis of pontoon-type very large floating structures (VLFS) considering directional wave spectra. The analysis is performed in the frequency domain using modal expansion to represent the floating structure's motion and the water's velocity potential. Response spectra are computed using random vibration analysis assuming the directional wave spectrum can be described as a Gaussian process. The distribution of extremes is estimated to obtain mean extreme response values relevant for design. The method is demonstrated on an example VLFS to investigate the effect of mean wave angle on the stochastic response.
This document summarizes the research investigating the effect of longitudinal atmospheric turbulence on the dynamics of an airfoil with a structural nonlinearity in pitch. Three different regions of dynamic behavior are observed when the airfoil is excited by longitudinal turbulence, compared to two regions for the nonexcited case. A new region exists where the airfoil response is concentrated about the equilibrium position, attributed to the parametric nature of the turbulence excitation. Utter occurs at a lower velocity and limit cycle oscillations occur at a higher velocity for the excited case versus the nonexcited case. The airfoil and aerodynamic models used in the numerical simulations are described.
This document discusses forced harmonic motion modelling. It describes free vibration versus forced vibration, undamped versus damped systems, and common spring, mass, and damping elements. It provides the example of the 1940 collapse of the Tacoma Narrows Bridge due to resonant wind forces that matched the bridge's natural frequency. The document outlines modelling a spring-mass system to represent a real system and describes external forcing, base excitation, and rotor excitation models. It concludes with the equation of motion for an externally forced system using Newton's laws of motion.
Lattice boltzmann simulation of non newtonian fluid flow in a lid driven cavitIAEME Publication
This document summarizes a study that uses Lattice Boltzmann Method (LBM) to simulate non-Newtonian fluid flow in a lid driven cavity. The study explores the mechanism of non-Newtonian fluid flow using the power law model to represent shear-thinning and shear-thickening fluids. It investigates the influence of power law index and Reynolds number on velocity profiles and streamlines. The LBM code is validated against published results and shows agreement with established theory and fluid rheological behavior.
1. The document discusses various topics in waves, optics, oscillation, and gravitation including traveling waves, standing waves, wave propagation, simple harmonic motion, Newton's laws of gravity, and key terms.
2. Examples are provided to demonstrate calculations for spring oscillation, wave speed in a string, pendulum motion, and gravitational acceleration based on pendulum period.
3. Formulas are listed for spring constant, frequency, wave velocity, and other important relationships.
1. The document discusses various topics related to waves, optics, oscillation, and gravitation. It defines key terms like traveling waves, standing waves, and wave propagation.
2. Important concepts are covered, including the principle of superposition, simple harmonic motion, Newton's laws of gravitation, and Kepler's laws of planetary motion.
3. Examples are provided to demonstrate applications of these concepts, such as calculating spring oscillation properties and determining values related to a vibrating string and pendulum motion.
What are the most viable forms of alternative propulsion for the future of sp...Wilfrid Somogyi
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Similar to FINAL PAPER Vibration and Stochastic Wave Response of a TLP (20)
3. 3
Table 1- Nomenclature
Symbol Meaning Value
L Length 260 m
ϕ Random Variable [0, ∞)
π Pi 3.1415
τ Time constant Seconds
t Time [0, ∞) seconds
k Torsional stiffness 100 kN•m
c Viscous Damping 3.036 x 1010 kg•m/s
ω Frequency [range of values] rad/s
ωn Natural Frequency [range of values] rad/s
ωo Initial Frequency (when
n=0)
[range of values] rad/s
m Mass 169,353 kg
A Amplitude 2000 N
θ Angle (of motion) Radians
N Upper Limit ∞
Boldfaced values are borrowed from [5]
2.2 Identification of the Input Forces
It is necessary to derive the input force on the system. The autocorrelation
function of this force can than be found. The ocean waves can be modeled as a
stochastic, harmonic force that acts on the system. The different natural frequencies
need to be added together because they contribute to the overall force. A random
variable generator can be used to create the random variable that is within the same
range as the natural frequency. It does not matter if the random variable is added or
subtracted.
(1)
Although the cosine function is used here, the sine function can be used as well. The
upper limit can be adjusted based on how many frequency values need to be
evaluated. It should be noted that the natural frequency is defined as:
(2)
Where T is a fixed time period, but n if from the range of 0, 1, 2,..N.