Dynamic Reanalysis of Structures Based on Differential Geometric Method (1st Report)

Basic Theory

Abstract

A new method is proposed to evaluate the dynamic characteristics of a re-designed structure by using those of the original structure. The method is developed based on perturbation method in such a way that first the differential equations which describe the change of dynamic characteristics of being modified structure are derived by using perturbation method and then the solution curves of the equations are traced by those of the standard equations on manifold of special orthogonal group. The method has features that it can give clear correspondence between the eigenpairs before and after structural modification and that the computer run time is far shorter than that of conventional finite element analysis when only the selected few modes are used in the approximate computation. In addition, this approximate computation can give more accurate results than the perturbation method. Efficiency of the method is verified by a 600 degrees-of-freedom model which receives structural modification.