Elastic Waves in Anisotropic Laminates

ISBN-13: 9780849310706 / Angielski / Twarda / 2001 / 472 str.

G. R. Liu; Z. C. Xi

Opis

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.

Spis treści

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

O autorze

G.R. Liu