Elastic waves in anisotropic laminates

TLDR: In this article, the authors describe a technique for the Inverse Fourier Integration Response in Time Domain Poles and Complex Paths of a WAVs in the Wavenumber Domain.

Abstract: 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