A novel order reduction method for nonlinear dynamical system under external periodic excitations
Motivated by the concept of nonlinear Galerkin method and the port-processed Galerkin method for the reduction of large-scale dynamical system, a novel order reduction method (Method I) for order reduction of nonlinear system under external periodic excitation has been proposed to balance the accuracy of the dynamical responses and the computational cost. After a modal transformation, the large dynamical system is split into a master subsystem, a plane subsystem and a negligible subsystem. As a comparison, Method II accounting for the effects of bold ``slave'' subsystem and the ``negligible'' subsystem has also been developed to obtain the reduced order subsystem. A 5-degree-of-freedom nonlinear oscillator has been given as an example to illustrate the reduction procedure of the system. The numerical results show that Method I gives a considerable increase in accuracy for little computational cost in comparison with the standard Galerkin method, and produces about the same accuracy as Method II. Large-scale dynamical systems in practical engineering, because of the dimension of the negligible subsystem using Method II, will have much more computational cost in comparison with using the standard Galerkin method.
scientific article; zbMATH DE number 5770128