Wavelet methods for dynamical problems: with application to metallic, composite, and nano-composite structures

"Considering that wavelet transforms have 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." "Available 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 wave equations related to structural dynamics, a topic that has not been sufficiently explored in the literature to this point. 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. 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."--Jacket.

Introduction -- Integral transform methods -- Structural dynamics : introduction and wavelet transform -- Wave propagation : spectral analysis -- Wavelet spectral finite element : time domain analysis -- Wavelet spectral finite element : frequency domain analysis -- Wavelet spectral finite element : two-dimensional structures -- Vibration and wave propagation in carbon nanotubes -- Vibration and wave propagation in nano-composites -- Inverse problems.