Nonlinear Dynamics by Mode Superposition.

摘要

A mode superposition technique for approximately solving nonlinear initial-boundary-value problems of structural dynamics is discussed and results,for examples involving large deformation,are compared to those obtained with implicit direct integration methods,such as the Newmark generalized acceleration and Houbolt backward-difference operators. The initial natural frequencies and mode shapes are found through inverse power iteration,with the trial vectors for successively higher modes being swept by Gram-Schmidt orthonormalization at each iteration. The subsequent modal spectrum for nonlinear states is based upon the tangent stiffness of the structure and is calculated by a subspace iteration procedure that involves matrix multiplication only,using the most recently computed spectrum as an initial estimate. The results indicate that a number of important advantages accrue to nonlinear mode superposition. (Modified author abstract)