Parametric instability of conical shells by the Generalized Differential Quadrature method

The analysis of cylindrical shells using an improved version of the differential quadrature method is presented. The generalized differential quadrature (GDQ) method has computational advantages over the existing differential quadrature method. The GDQ method has been applied in solutions to fluid dynamics and plate problems and has shown superb accuracy, efficiency, convenience, and great potential in solving differential equations. The present article attempts to apply the method to the solutions of cylindrical shell problems. To illustrate the implementation of the GDQ method, the frequencies and fundamental frequencies for simply supported-simply supported, clamped-clamped, and clamped-simply supported boundary conditions are determined. Results obtained are validated by comparing them with those in the literature.

Parametric instability of thin, circular cylindrical shells subjected to in-plane longitudinal inertia loading arising from sinusoidal base excitation has been investigated analytically and experimentally. The shell under consideration was rigidly clamped at the base and free at the upper edge. In the applied excitation frequency range, the test specimens exhibited lateral vibrations, at half the driving frequency, with one half longitudinal wave and three full circumferential waves. The linear bending theory used in the analysis was adequate in predicting the incipience of instability, just as in the case of slender rods. Attention has been confined to investigating only the principal instability region, as observed during the experiments. Excellent agreement was obtained between the analytical and experimental results.