Wavelet Methods for Dynamical Problems : With Application to Metallic, Composite, and Nano-Composite Structures book cover
1st Edition

Wavelet Methods for Dynamical Problems
With Application to Metallic, Composite, and Nano-Composite Structures

ISBN 9781439804612
Published March 17, 2010 by CRC Press
304 Pages 129 B/W Illustrations

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Book Description

Employs a Step-by-Step Modular Approach to Structural Modeling

Considering that wavelet transforms have also proved useful in the solution and analysis of engineering mechanics problems, up to now there has been no sufficiently comprehensive text on this use. Wavelet Methods for Dynamical Problems: With Application to Metallic, Composite and Nano-composite Structures addresses this void, exploring the special value of wavelet transforms and their applications from a mechanical engineering perspective. It discusses the use of existing and cutting-edge wavelet methods for the numerical solution of structural dynamics and wave propagation problems in dynamical systems.

Existing books on wavelet transforms generally cover their mathematical aspects and effectiveness in signal processing and as approximation bases for solution of differential equations. However, this book discusses how wavelet transforms are an optimal tool for solving ordinary differential equations obtained by modeling a structure. It also demonstrates the use of wavelet methods in solving partial differential equations related to structural dynamics, which have not been sufficiently explored in the literature to this point.

Presents a new wavelet based spectral finite element numerical method for modeling one-, and two-dimensional structures

Many well-established transforms, such as Fourier, have severe limitations in handling finite structures and specifying non-zero boundary/initial conditions. As a result, they have limited utility in solving real-world problems involving high frequency excitation. This book carefully illustrates how the use of wavelet techniques removes all these shortcomings and has a potential to become a sophisticated analysis tool for handling dynamical problems in structural engineering.

Covers the use of wavelet transform in force identification and structural health monitoring

Designed to be useful for both professional researchers and graduate students alike, it provides MATLABĀ® scripts that can be used to solve problems and numerical examples that illustrate the efficiency of wavelet methods and emphasize the physics involved.

Table of Contents

Solution of structural dynamics problem
Solution of wave propagation problem
Objective and outline of the book
Integral Transform Methods
Laplace transform
Fourier transform
Wavelet transform
Structural Dynamics: Introduction and Wavelet Transform
Free vibration of single degree of freedom systems
Forced vibration of SDOF system
Harmonic loading
Response to arbitrary loading
Response of SDOF through wavelet transform
Free vibration of multi degree of freedom system
Modal analysis for forced vibration response of MDOF
Response of MDOF system using wavelet transform
Wave Propagation: Spectral Analysis
Spectrum and dispersion relations
Computations of wavenumbers and wave amplitudes
Spectral finite element (SFE) method
FSFE formulation of Timoshenko beam
FSFE formulation of isotropic plate under in-plane loading
Wavelet Spectral Finite Element: Time Domain Analysis
Reduction of wave equations for a rod
Decoupling using eigenvalue analysis
Wavelet spectral finite element formulation for a rod
Time domain response of elementary rod under impulse load
Reduction of wave equations for Euler-Bernoulli beam
WSFE formulation for Euler-Bernoulli beam
Time domain response of Euler-Bernoulli beam under impulse load
Wave propagation in frame structure
Governing differential wave equations for higher order composite beam
WSFE formulation for composite beam
Time domain response of higher order composite beam
Wavelet Spectral Finite Element: Frequency Domain Analysis
Frequency domain analysis: periodic boundary condition
Computation of wavenumbers and wave speeds
Constraint on time sampling rate
Wavelet Spectral Finite Element: Two-Dimensional Structures
Governing differential wave equations for isotropic plate
Reduction of wave equations through temporal approximation
Reduction of wave equations through spatial approximation
Wavelet spectral finite element for plate
Wave propagation in isotropic plates
Governing differential wave equations for axisymmetric cylinder
Bessel function solution for axisymmetric cylinder
Wave Propagation in isotropic axisymmetric cylinders
Vibration and Wave Propagation in Carbon Nanotubes
Carbon nanotubes: introduction
Axisymmetric shell model of single-walled carbon nanotubes
Thin shell model of multi-walled carbon nanotubes
Frequency domain analysis|
Time domain analysis
Vibration and Wave Propagation in Nano-Composites
Introduction: nano-composites
Beam model of MWNT embedded nano-composite
Spectral finite element formulation for MWNT embedded nanocomposite beam
Frequency domain analysis
Time domain analysis
Shell model of SWNT-polymer nano-composite
Time domain analysis
Inverse Problems
Force reconstruction
Numerical examples of impulse force reconstruction
Damage modeling and detection
Modeling of de-lamination in composite beam
Damage detection and de-noising using wavelet analysis
Wave propagation in delaminated composite beam and damage detection

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Dr. S. Gopalakrishnan is a professor in the Department of Aerospace Engineering at Indian Institute of Science, Bangalore. Dr. M. Mitra is an assistant professor in the Department of Aerospace Engineering at Indian Institute of Technology Bombay, Mumbai.