DYNAMIC MODAL TRUNCATION-RELAXATION

摘要

The present paper deals with mechanical systems containing elastic bodies. In writing equations governing motions of such systems, use is frequently made of the assumed modes theory to describe elastic deflections of elastic bodies. When simulations of motions are run by numerically integrating the indicated equations, the number of modes is determined a-priori. A method, called dynamic modal truncation- relaxation, is introduced here, whereby modes can be either truncated or relaxed at each integration step. The method is applied to a specific example and a simulation code is constructed, showing that a significantly improved balance can be obtained between simulation efficiency (i.e., execution time) and simulation accuracy, as compared with the balance obtained with an a-priori chosen number of modes. The method is useful when simulation run-time is of importance, e.g., when real-time simulations are performed in the context of control design; when many simulations have to performed in the context of a parameter study; or, when missions of long duration have to be simulated rapidly, as in designing a new course for a spacecraft already in motion.