Numerical Simulation Research On Dynamics Of A String-beam Coupled Nonlinear Vibration System

Normally,the exact solution of the nonlinear coupling system is difficult to obtain.So,the analytic approximation of this problem becomes the object of study for many scholars.In recent years,many approximate analytic methods have been found,including average method,multi-scale method,harmonic balance method and KBM asymptotic method.Because the multiple-scale method divides the time scale more precisely,it has higher computation precision and wide application.This paper studies nonlinear dynamic behavior of a string-beam coupled system sub-jected to parametric and external excitations.Firstly,the method of multiple scales is used to analyze the nonlinear responses of the string-beam system coupled system.Sec-ondly,based on the average equation and taking the damping coefficient of the system as the bifurcation parameter,the stability of the equilibrium point of the system is an-alyzed and the bifurcation curve of the equilibrium point is obtained.In order to verify the correctness of theoretical prediction,the trajectories in phase space under different bifurcation parameters are simulated.Finally,the four-order Runge-Kutta algorithm is utilized to verify the existence of the chaotic motions in the string-beam coupled sys-tem.From the results of numerical simulation,it is clearly found that the system exists period-1 motion,multi-periodic motion and chaotic motion.