An applied model for free radial vibrations of a closed spherical sandwich shell

Abstract

Free vibrations across the thickness of a closed spherical shell are studied. A finite solution to the one-dimensional (along the radius) wave problem is derived for the shell, which differs from the solution for radial vibrations of a liquid. The solution is used in constructing a model for joint vibrations of three spherical layers. An approximate version of their vibratory motion is suggested, which is based on a shell model with thin stiff layers enveloping a thick soft core layer. The solution to the dynamic problem of free vibrations of the soft core is obtained by the method of separation of variables. The elastic reactions of the thin face layers were taken as boundary conditions, which allowed us to reduce the dynamics of the three layers to a vibratory motion of the midlayer under mixed boundary conditions. A transcendental equation for eigenvalues of the problem on free vibrations is derived and analyzed. A graphic description of the effect of layer thickness and elastic properties on the spectrum of eigenvalues of the mixed boundary problem is represented. Relationships for the main eigenfrequency versus the stiffness of face layers and characteristic geometric parameters of the sandwich shell wall are obtained.