Numerical analysis of the eigenfrequency spectrum of shells of revolution (Q1128402)

Shell structures are normally subject to vibrations and may break down in a certain frequency range. It is mainly the size of the shell that determines whether or not its eigenfrequencies remain in the safe interval that guarantees stability. A method is proposed for studying the distribution of eigenvalues of a shell of revolution as a function of shell size and thickness. The mathematical model is based on the system of differential equations describing the normal modes of a thin elastic shell of revolution. Discretization of the original system by the integral identity approximation method gives a second-order accurate difference scheme which preserves real and sign-definite eigenvalues. The dependence of eigenvalues on two additional parameters characterizing shell size and thickness is analyzed by a version of the \(D\)-partition numerical method. Numerical results are reported for shells in the shape of a truncated cone and a toroidal belt.