METHOD FOR CALCULATING THE NATURAL FREQUENCIES AND MODES OF A THICK-WALLED CYLINDRICAL SHELL

摘要

To calculate the natural frequencies and modes of a homogeneous axisymmetric cylinder with thickness commensurable with its length and radius, it is necessary to solve a three-dimensional problem of dynamic elasticity.rnThis problem is reduced to a system of two-dimensional (in spatial coordinates) dynamic equations and boundary conditions in the radial coordinate by the generalized method of finite integral transforms [2]. Fourier series expansion in powers of the circumferential coordinate is used to reduce the resulting problem to a sequence of systems of one-dimensional (in a spatial coordinate) differential equations (one system for each harmonic).