Dynamic analysis of nonlinear systems by modal synthesis techniques

Abstract

Different kinds of modal synthesis method have been used widely in dynamic analysis of linear structure systems, but, in general, they are not suitable for nonlinear systems.

In this paper, a kind of modal synthesis techniques is extended to dynamic analysis of nonlinear systems. The procedure is based upon the method suggested in [20], [21], which is applicable to vibration analysis for complex structure systems with coupling attachments but with simplified forms of linear springs and dampers. In fact, these attachments have nonlinear characteristics as those generally known to the cases of nonlinear elasticity and nonlinear damping, e.g., piecewise-linear springs, softening or hardening springs, Coulomb damping, elastoplastic hysteresis damping, etc.. So long as the components of structure are still linear systems, we can get a set of independent free-interface normal mode information but only keep the lower-order for each component. This can be done by computations or experiments or both. The global equations of linear vibration are set up by assembling of the component equations of motion with nonlinear coupling forces of attachments. Then the problem is reduced to less degrees of freedom for solving nonlinear equations. Thus considerable saving in computer storage and execution time can be expected. In the case of a very high-order system, if sufficient degrees of freedom are reduced, then it may be possible for the problem to be solved by the aid of a computer of ordinary grade.

As the general nonlinear vibration of multiple degrees of freedom systems is quite involved, in general, the exact solution of a nonlinear system equations is not easy to find, so the numerical method can be adopted for solving the reduced nonlinear equations to obtain the transient response of system for arbitrary excitations.