Principal waves in orthotropic elastic membranes (Q1076540)

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.