1st Edition

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

By S. Gopalakrishnan, Mira Mitra Copyright 2010
    304 Pages 129 B/W Illustrations
    by CRC Press

    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.

    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


    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.