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

Wavelet Methods for Dynamical Problems

With Application to Metallic, Composite, and Nano-Composite Structures, 1st Edition

By S. Gopalakrishnan, Mira Mitra

CRC Press

298 pages | 129 B/W Illus.

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pub: 2010-03-17
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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 MATLAB® 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



About the Authors

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.

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Mechanics / General