Nonlinear supersonic flutter of truncated conical shells

摘要

A numerical model was developed to investigate the flutter instability of truncated conical shells subjected to supersonic flows. The exact solution of Sanders' best firstorder approximation was used to develop the finite elements model of the shell. Nonlinear kinematics of Donnell's, Sanders' and Nemeth's theories, in conjunction with the generalized coordinates method, were used to formulate the nonlinear strain energy of the shell. A pressure field was formulated using the piston theory with the correction term for the curvature. Lagrangian equations of motion based on Hamilton's principle were obtained. A variation of the harmonic balance method was used for developing the amplitude equations of the shell, and a numerical method was used for solving these equations. Results of linear and nonlinear flutter of truncated conical shells were validated against the existing data in the literature. It was observed that geometrical nonlinearities have a softening effect on the stability of the shell in supersonic flows.