Method of Polynomial Vectors for Solving Nonlinear Vibrations with Multiple Time Scales
Dongping Jin
Abstract:This paper gives a method for solving nonlinear vibration of multiple degrees of freedom system using the polynomial vectors. The nonlinear equations of motion of ordinary differential form are represented firstly by their state equations, and then a set of non-homogeneous perturbation equations of nonlinear system is obtained using the multiple time scales. The approximate solutions of the non-homogeneous equations are directly given by the linearized equations and their nonlinear parts using just one-step calculation, which provides all solutions of system. Accordingly, the secular terms related to resonances exist in the integral part of the approximate solutions. Finally, a two-dimension oscillator of cubic nonlinearity and a four-dimension spring-pendulum are taken as examples to demonstrate the solution process of the proposed method.
文章链接：https://link.springer.com/article/10.1007/s42417-024-01353-9
