A general substructure synthesis method for the dynamic simulation of complex structures

In this paper a general substructure synthesis method is developed for the dynamic analysis of complex flexible structures. The motion of each substructure is represented by a given number of substructure admissible functions. Substructure admissible functions are often low-order polynomials, and hence computationally easy to work with. The otherwise disjoint substructures are connected together to form a whole structure by imposing approximate geometric compatibility conditions by means of the method of weighted residuals. The behavior of the estimated eigenvalues obtained by the substructures synthesis method can be ascertained by means of a bracketing theorem. The estimated eigenvalues do converge to the actual eigenvalues of the original structure, although it is necessary to consider two limiting processes, one in which the number of substructure admissible functions is increased and the other in which the number of internal boundary weighting functions is increased.