AN ALGORITHM FOR SIMULATION OF NONLINEAR MECHANICAL SYSTEMS USING ENERGY AND FORCE SIMILARITY OF ITS ELEMENTS

An algorithm, based upon energy and force equilibrium, is proposed to evaluate the frequency response characteristics of nonlinear mechanica l systems with symmetric and asymmetric dissipative and restoring elem ents. Dual stage dampers and hardening springs with symmetric or asymm etric characteristics are characterized by an array of local equivalen t linear coefficients, using the methodology based upon principle of e nergy similarity. Frequency response characteristics of a dynamical sy stem comprising nonlinear symmetric and asymmetric damping and hardeni ng spring are evaluated, and compared to those determined from direct integration of the nonlinear system equations. An error analysis is pe rformed to determine the magnitude of error between the nonlinear and local equivalent linear forces. The average force error is then integr ated within the local equivalent algorithm to achieve the force simila rity between the nonlinear and linear elements. The results revealed t hat the proposed algorithm can accurately estimate the frequency respo nse characteristics of the nonlinear systems in a highly efficient man ner. The algorithm based upon energy similarity alone yields slight er ror near the resonant frequencies, while the analysis based on the com bined energy and force similarity can reduce this error considerably.