Effect of a nonstationary acoustic wave on a cylindrical orthotropic shell

Abstract

Study of the nonstationary deformation of thin-walled structure elements subjected to waves in an acoustic medium (an ideal compressible fluid or gas) has advanced significantly in recent years. The fundamental results obtained in this area are shown in the monographs [6, 8, 15, 16] and in the survey [5]. The overwhelming majority of these investigations concern isotropic plates and shells. At the same time, in connection with the much broader utilization of glass--plastic materials and thin-walled structure elements using them in the most diverse branches of engineering and machine construction, investigation of shocks on such objects has become urgent. Some of the most important objects from the practical viewpoint are multilayered cylindrical shells. In this area, we should note [7-10]. The effect of a plane step wave on an infinite elastic cylindrical shell reinforced by a number of periodically arranged ribs is examined in [9]. Approximate relations to describe the interaction between the obstacle and the medium are used in analyzing the transients in the papers mentioned. The present paper is devoted to an investigation of the nonstationary deformation of an orthotropic cylindrical shell subjected to a plane step wave whose front is parallel to the shell generatriz. A method consisting of the application of the Laplace integral transform and its subsequent inversion by using a Volterra integral equation for each of the vibrations modes is used to solve the problem. This method had been used earlier to solve nonstationary hydroelasticity problems for cylindrical and spherical bodies [2, 12, 13, 14]. 1. An infinite circular cylindrical shell submerged in an acoustic medium is considered. It is assumed that the shell material is cylindrically srthstropic, i.e., its elastic properties in the generatrix and directrix directions are distinct. We use the equations, presented in [1], but supplemented by inertial terms, to describe the elastic deformation of the shell. We hence limit ourselves at once to the case of plane deformation. We will have