An exact series solution for free vibration of cylindrical shell with arbitrary boundary conditions

Abstract

Simple accurate formulas for the natural frequencies of circular cylindrical shells are presented for modes in which transverse deflection dominates. Based on the Donnell-Mushtari thin shell theory the equations of motion of the circular cylindrical shell are introduced, using series expansion for axial coordinate and Fourier series for the circumferential direction, a simple explicit solution is obtained. Also, the influence of deformation component is investigated, it is shown that it can be neglected. Good agreement with experimental data and FEM is shown. The advantage of a current approach over the existing formulas is simplicity in programming.

A simple tool to forecast the natural frequencies of thin-walled cylinders

“…The integration of the partial differential equations rarely leads to an exact closed-form solution, which, however, is rather convoluted [1]. More frequently, the resolution is achieved by finite element analysis, numerical approaches [1][2][3][4][5][6][7] or simplified analytical models [8][9][10][11][12]. Nonetheless, the finite element method (FEM) may require a convergence analysis and lacks intelligibility.…”