Group velocity and characteristic wave curves of Lamb waves in composites: Modeling and experiments

Modelling of wave propagation in composite plates using the time domain spectral element method

This paper reviews the state-of-the-art in numerical wave propagation analysis. The main focus in that regard is on guided wave-based structural health monitoring (SHM) applications. A brief introduction to SHM and SHM-related problems is given, and various numerical methods are then discussed and assessed with respect to their capability of simulating guided wave propagation phenomena. A detailed evaluation of the following
methods is compiled: (i) analytical methods, (ii) semi-analytical methods, (iii) the local interaction simulation approach (LISA), (iv) finite element methods (FEMs), and (v) miscellaneous methods such as mass–spring lattice models (MSLMs), boundary element methods (BEMs), and fictitious domain methods. In the framework of the FEM, both time and frequency domain approaches are covered, and the advantages of using high order shape functions are also examined.

Simulation Methods for Guided Wave-Based Structural Health Monitoring: A Review

Time–transient response for ultrasonic guided waves propagating in damped cylinders

The Green's function (GF) method, which makes use of GFs, is an important and elegant tool for solving a given boundary-value problem for the differential equation from a real engineering or physical field. Under a concentrated source, the solution of a differential equation is called a GF, which is singular at the source location, yet is very fundamental and powerful. When looking at the GFs from different physical and/or engineering fields, i.e. assigning the involved functions to real physical/engineering quantities, the GFs can be scaled and applied to large-scale problems such as those involved in Earth sciences as well as to nano-scale problems associated with quantum nanostructures. GFs are ubiquitous and everywhere: they can describe heat, water pressure, fluid flow potential, electromagnetic (EM) and gravitational potentials, and the surface tension of soap film. In the undergraduate courses Mechanics of Solids and Structural Analysis, a GF is the simple influence line or singular function. Dropping a pebble in the pond, it is the circular ripple traveling on and on. It is the wave generated by a moving ship in the opening ocean or the atom vibrating on a nanoscale sheet induced by the atomic force microscopy. In Earth science, while various GFs have been derived, a comprehensive review is missing. Thus, this article provides a relatively complete review on GFs for geophysics. In section 1, the George Green's potential functions, GF definition, as well as related theorems and basic relations are briefly presented. In section 2, the boundary-value problems for elastic and viscoelastic materials are provided. Section 3 is on the GFs in full- and half-spaces (planes). The GFs of concentrated forces and dislocations in horizontally layered half-spaces (planes) are derived in section 4 in terms of both Cartesian and cylindrical systems of vector functions. The corresponding GFs in a self-gravitating and layered spherical Earth are presented in section 5 in terms of the spherical system of vector functions. The singularity and infinity associated with GFs in layered systems are analyzed in section 6 along with a brief review of various layer matrix methods. Various associated mathematical preliminaries are listed in appendix, along with the three sets of vector function systems. It should be further emphasized that, while this review is targeted at geophysics, most of the GFs and solution methods can be equally applied to other engineering and science fields. Actually, many GFs and solutions methods reviewed in this article are derived by engineers and scientists from allied fields besides geophysics. As such, the updated approaches of constructing and deriving the GFs reviewed here should be very beneficial to any reader.

https://iopscience.iop.org/article/10.1088/1361-6633/ab1877/pdf

Green’s functions for geophysics: a review

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

Y Horie

Papers

Elastic waves in anisotropic laminates