Principal waves in orthotropic elastic membranes
type: Item
instance of: scholarly article
title: Principal waves in orthotropic elastic membranes
zbMATH Open document ID: 0593.73025
DOI: 10.1007/BF00250728
author: B. George
published in: Archive for Rational Mechanics and Analysis
publication date: 1985-01-01T00:00:00Z
review text: Bowen and Wang dealt with propagation of waves in isotropic elastic (three-dimensional) material bodies [\textit{R. M. Bowen} and the second author, ibid. 38, 13-45 (1970; Zbl 0206.540)] and subsequently extended these results to waves in orthotropic elastic material bodies [\textit{R. M. Bowen} and the second author, ibid. 47, 149-170 (1972; Zbl 0249.73032)]. In the present paper, the authors use the same ideas, extending to orthotropic elastic membranes the results obtained previously by Pop and Wang for acceleration waves in isotropic elastic membranes [\textit{J. J. Pop} and the second author, ibid. 77, 47-93 (1981; Zbl 0513.73077)]. The field of response functions and their gradients, propagation conditions and amplitude equations have been derived. Special attention was given to principal waves, whose amplitude vectors are either parallel or orthogonal to their direction of propagation, obtaining thus longitudinal waves, shear waves and transverse waves. It is shown that the amplitude equations for principal shear waves, principal longitudinal waves, and principal transverse waves in orthotropic elastic membranes have the same form as the corresponding ones for principal waves in isotropic elastic membranes. Furthermore, the amplitude equations for principal shear waves and for principal transverse waves have exactly the same form.
Mathematics Subject Classification ID: 74J10
Mathematics Subject Classification ID: 74K15
Mathematics Subject Classification ID: 74E10
zbMATH DE Number: 3954368
zbMATH Keywords: orthotropic elastic membranes
zbMATH Keywords: field of response functions
zbMATH Keywords: gradients
zbMATH Keywords: propagation conditions
zbMATH Keywords: amplitude equations
zbMATH Keywords: principal waves
zbMATH Keywords: amplitude vectors
zbMATH Keywords: parallel
zbMATH Keywords: orthogonal
zbMATH Keywords: direction of propagation
zbMATH Keywords: longitudinal waves
zbMATH Keywords: shear waves
zbMATH Keywords: transverse waves
reviewed by: Petre P. Teodorescu
MaRDI profile type: Publication
cites work: Acceleration waves in isotropic elastic membranes
cites work: Acceleration waves in inhomogeneous isotropic elastic bodies
cites work: Acceleration waves in orthotropic elastic materials
cites work: On the response and symmetry of elastic and hyperelastic membrane points
cites work: On compatibility conditions for singular surfaces
cites work: Principal waves in elastic subfluids
cites work: A note on hyperelasticity
description: scientific article; zbMATH DE number 3954368