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

CRC Press, Mar 17, 2010 - Science - 298 pages

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 MATLABŪ scripts that can be used to solve problems and numerical examples that illustrate the efficiency of wavelet methods and emphasize the physics involved.

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### Contents

 Introduction 1 Integral Transform Methods 9 Structural Dynamics Introduction and Wavelet Transform 37 Wave Propagation Spectral Analysis 63 Wavelet Spectral Finite Element Time Domain Analysis 81 Wavelet Spectral Finite Element Frequency Domain Analysis 117 Wavelet Spectral Finite Element TwoDimensional Structures 141
 Vibration and Wave Propagation in Carbon Nanotubes 183 Vibration and Wave Propagation in NanoComposites 207 Inverse Problems 241 References 265 Index 273 Copyright