A theory of pulse propagation in anisotropic elastic solids
type: Item
instance of: scholarly article
title: A theory of pulse propagation in anisotropic elastic solids
zbMATH Open document ID: 0621.73032
DOI: 10.1016/0165-2125(87)90020-5
author: Andrew N. Norris
published in: Wave Motion
publication date: 1987-01-01T00:00:00Z
review text: A theory is described for the propagation of pulses in anisotropic elastic media. The pulse is initially defined by a harmonically modulated Gaussian envelope. As it propagates the pulse remains Gaussian, its spatial form characterized by a complex-valued envelope tensor. The center of the pulse follows the ray path defined by the initial velocity direction of the pulse. Relatively simple expressions are presented for the evolution of the amplitude and phase of the pulse in terms of the wave velocity, the phase slowness and unit displacement vectors. The spreading of the pulse is characterized by a spreading matrix. Explicit equations are given for this matrix in a transversely isotropic material. The rate of spreading can vary considerably, depending upon the direction of propagation. New reflected and transmitted pulses are created when a pulse strikes an interface of material discontinuity. Relations are given for the new envelope tensors in terms of the incident pulse parameters. The theory provides a convenient method to describe the evolution and change of shape of an ultrasonic pulse as it traverses a piecewise homogeneous solid. Numerical simulations are presented for pulses in a strongly anisotropic fiber reinforced composite.
Mathematics Subject Classification ID: 74J99
Mathematics Subject Classification ID: 74E10
Mathematics Subject Classification ID: 74J20
zbMATH DE Number: 4007812
zbMATH Keywords: general Gaussian wave packet solution
zbMATH Keywords: reflection/transmission problem
zbMATH Keywords: propagation of pulses
zbMATH Keywords: harmonically modulated Gaussian envelope
zbMATH Keywords: complex- valued envelope tensor
zbMATH Keywords: evolution of the amplitude
zbMATH Keywords: phase
zbMATH Keywords: wave velocity
zbMATH Keywords: phase slowness
zbMATH Keywords: unit displacement vectors
zbMATH Keywords: spreading matrix
zbMATH Keywords: transversely isotropic material
zbMATH Keywords: change of shape
zbMATH Keywords: ultrasonic pulse
zbMATH Keywords: piecewise homogeneous solid
zbMATH Keywords: strongly anisotropic fiber reinforced composite
MaRDI profile type: Publication
full work available at URL: 0165-2125(87)90020-5
OpenAlex ID: W2034842912
cites work: Q5598977
cites work: The Cauchy problem for elastic waves in an anisotropic medium
cites work: Q3692956
cites work: Gaussian wave packets in inhomogeneous media with curved interfaces
cites work: Q4745347
cites work: Elastic Gaussian wave packets in isotropic media
cites work: Q5652388
cites work: A Mixture Model for Unidirectionally Fiber-Reinforced Composites
cites work: Elastic waves in anisotropic media
description: scientific article; zbMATH DE number 4007812