Free vibrations of a spherical shell with a pinched edge

Abstract

Shells as elements of machines and structures are widely used in aircraft shipbuilding and engineering. Shells as elements of machines and structures are widely used in aviation, shipbuilding and various fields of engineering and technology. In this paper the problem of free vibrations of a spherical shell with a pinched edge is considered. The equations of oscillations of a thin elastic spherical shell with a pinched edge are given. The solution is expressed through Lejandre and exponential functions. Based on the methods of special functions of mathematical physics, Mueller method and Gauss method, an algorithm for solving the problem on a computer is developed. An engineering method for determining the natural frequencies of a spherical shell with a pinched edge is proposed. Numerical results are obtained on the basis of the constructed frequency equations with complex input parameters.