1st Edition

Elastic Waves in Anisotropic Laminates

By G.R. Liu, Z. C. Xi Copyright 2002
    470 Pages 170 B/W Illustrations
    by CRC Press

    Ultrasonic non-destructive evaluation (NDE) plays an increasingly important role in determining properties and detecting defects in composite materials, and the analysis of wave behavior is crucial to effectively using NDE techniques. The complexity of elastic wave propagation in anisotropic media has led to a reliance on numerical methods of analysis-methods that are often quite time-consuming and whose results yield even further difficulties in extracting explicit phenomena and characteristics.

    Innovative and insightful, Elastic Waves in Anisotropic Laminates establishes a set of high-performance, analytical-numerical methods for elastic wave analysis of anisotropic layered structures. The treatment furnishes a comprehensive introduction, sound theoretical development, and applications to smart materials, plates, and shells. The techniques, detailed in both the time and frequency domains, include methods that combine the finite element method (FEM) with the Fourier transform approach and the strip element method (SEM). These -methods can also be used for expediently finding the Green's function for anisotropic laminates useful for inverse problems related to wave propagation, and methods for inverse analyses, including conjugate gradient methods, and genetic algorithms are also introduced.

    The text is complemented by many examples generated using software codes based on the techniques developed. Filled with charts and illustrations, Elastic Waves in Anisotropic Laminates is accessible even to readers from non-engineering backgrounds and offers a unique opportunity to discover methods that can lead to an understanding of the dynamic characteristics and wave motion behaviors of advanced composite materials.

    FUNDAMENTS OF WAVES IN ELASTIC SOLIDS
    Introduction
    Formulation of Longitudinal Wave in a Bar
    Free Wave Motion in Infinite Bars
    Free Wave Motion in a Finite Bar
    Forces Wave Motion in an Infinite Bar
    Forced Wave Motion in a Finite Bar
    Transient Waves in an Infinite Bar
    Remarks
    WAVES IN PLATES OF FUNCTIONALLY GRADED MATERIAL
    Introduction
    Element of Linear Property Variation
    Boundary and Continuity Conditions
    Transient Response
    Evaluation of Confluent Hypergeometric Function
    Examples
    Remarks
    FREE WAVE MOTION IN ANISOTROPIC LAMINATES
    Introduction
    Basic Equations
    Derivation of Dispersion Equation
    Strain Energy Distribution
    Examples
    Remarks
    FORCED WAVE MOTION IN COMPOSITE LAMINATES
    Introduction
    Basic Equations
    Boundary and Interface Conditions
    Displacement in the Wavenumber Domain
    A Technique for the Inverse Fourier Integration
    Response in Time Domain
    Poles and Complex Paths
    Examples
    Remarks
    CHARACTERISTICS OF WAVES IN COMPOSITE LAMINATES
    Introduction
    Dispersion Equation
    Group Velocities
    Phase Velocity Surface
    Phase Slowness Surface
    Phase Wave Surface
    Group Velocity Surface
    Group Slowness Surface
    Group Wave Surface
    Examples
    Remarks
    FREE WAVE MOTION IN ANISOTROPIC LAMINATED BARS: FINITE STRIP ELEMENT METHOD
    Introduction
    System Equation
    Examples
    Remarks
    FREE WAVE MOTION IN COMPOSITE LAMINATED BARS: SEMI-EXACT METHOD
    Introduction
    System Equation
    Examples of Harmonic Waves in Bars
    Edge Waves in Semi-Infinite Laminates
    Remarks
    TRANSIENT WAVES IN COMPOSITE LAMINATES
    Introduction
    HNM Formulation
    Equation in Wavenumber Domain
    Displacement in Wavenumber Domain
    Response in Space-Time Domain
    Response to Line Time-Step Load
    Response to Point Time-Step Load
    Techniques for Inverse Fourier Integral
    Response to Transient Load of Arbitrary Time Function
    Remarks
    WAVES IN FUNCTIONALLY GRADED PLATES
    Introduction
    Dynamic System Equation
    Dispersion Relation
    Group Velocity
    Response Analysis
    Two-Dimensional Problem
    Computational Procedure
    Dispersion Curves
    Transient Response to Line Time-Step Loads
    Remarks
    WAVES IN ANISOTROPIC FUNCTIONALLY GRADED PIEZOELECTRIC PLATES
    Introduction
    Basic Equations
    Approximated Governing Equations
    Equations in Transform Domain
    Characteristics of Waves in FBPM Plates
    Transient Response Analysis
    Interdigital Electrodes Excitation
    Displacement and Electrostatics Potential Response
    Computation Procedure
    Dispersion Curves
    Excitation of Time-Step Shear Force in y Direction
    Excitation of a Line Electrode
    Excitation of Interdigital Electrodes
    Remarks
    STRIP ELEMENT METHOD FOR STRESS WAVES IN ANISOTROPIC SOLIDS
    Introduction
    System Equation
    SEM for Static Problems (Flamant's Problem)
    SEM for Dynamic Problems
    Remarks
    WAVE SCATTERING BY CRACKS IN COMPOSITE LAMINATES
    Introduction
    Governing Differential Equations
    Particular Solution
    Application of the SEM to Cracked Laminates
    Solution in the Time Domain
    Examples of Scattered Wave Fields
    Characterization of Horizontal Cracks
    Characterization of Vertical Surface-Breaking Cracks
    Characterization of Middle Interior Vertical Cracks
    Characterization of Arbitrary Interior Vertical Cracks
    Remarks
    WAVES SCATTERING BY FLAWS IN COMPOSITE LAMINATES
    Introduction
    Applications of the SEM to Plates Containing Flaws
    Examples for Wave Scattering in Laminates
    SH Waves in Sandwich Plates
    Strip Element Equation for SH Waves
    Particular Solution
    Complementary Solution
    General Solution
    SH Waves Scattered by Flaws
    Remarks
    BENDING WAVES IN ANISOTROPIC LAMINATED PLATES
    Introduction
    Governing Equation
    Strip element Equation
    Assembly of Element Equations
    Static Problems for Orthotropic Laminated Plates
    Wave Motion in Anisotropic Laminated Plates
    CHARACTERISTICS OF WAVES IN COMPOSITE CYLINDERS
    Introduction
    Basic Equations
    Dispersion Relations
    Examples Remarks
    WAVE SCATTERING BY CRACKS IN COMPOSITE CYLINDERS
    Introduction
    Basic Equations
    Axisymmetric Strip Element
    Examples
    Remarks
    INVERSE IDENTIFICATION OF IMPACT LOADS USING ELASTIC WAVES
    Introduction
    Two-dimensional Line Load
    Two-dimensional Extended Load
    Three-dimensional Concentrated Load
    Examples
    Remarks

    INVERSE DETERMINATION OF MATERIAL CONSTANTS OF COMPOSITE LAMINATES
    Introduction
    Inverse Operation
    Uniform-Micro Genetic Algorithms
    Examples
    Remarks

    Biography

    G.R. Liu