Semi-analytical and numerical solutions of multi-degree-of-freedom nonlinear oscillation systems with linear coupling

摘要

This research focuses on the development of an approach for solving multi-degree-of-freedom (MDOF) nonlinear oscillation problems with linear coupling. The original physical information included in the governing equations is mostly transferred into semi-analytical and numerical solutions. The semi-analytical solutions generated by the present approach are continuous everywhere and reflect more accurately the characteristics of the motion of the nonlinear dynamic systems. General procedures for three types of nonlinear oscillation problems are formulated in detail for allocation in nonlinear dynamic analysis. Two nonlinear oscillation systems with quadratic and cubic nonlinearities are solved to demonstrate the applications of the present approach.