EXACT MODAL SYNTHESIS TECHNIQUES USING RESIDUAL CONSTRAINT MODES

A new exact modal synthesis method for Þnding natural frequencies and modes of structures is proposed, in which the exact residual constraint modes based upon an incomplete set of normal modes of substructures with Þxed interfaces are expressed in two parts. These are the static constraint modes and a residual term with which it represents exactly the e¤ect of normal modes not retained. The modal synthesis uses a Ritz procedure and an iterative technique is presented for solving the non-linear equations of modal synthesis. This has the advantage that the results given by its Þrst iteration are exactly those given by the CraigÐBamptonÐHurty modal synthesis method, which leads to rapid convergence of subsequent iterations. The proposed method is an improvement of HuÕs exact modal synthesis method and is also shown to have as its limit the method of exact dynamic condensation. Numerical examples show that using the proposed method yields superior accuracy when only a few lower modes are used