Free vibration of a point-supported circular cylindrical shell

An analysis is presented for the free vibration of an elastically or rigidly point-supported circular cylindrical shell. For this purpose, the deflection displacements of the shell are written in a series of the deflection functions of beam. The dynamical energies of the shell are evaluated, and the frequency equation is derived by the Ritz method. For a rigidly point-supported shell, the Lagrangian multiplier method is conveniently employed. The method is applied to a cylindrical shell supported at symmetrically located four points; the natural frequencies and the mode shapes are calculated numerically, and the effects of the point supports on the vibration are studied.