Free vibration of vibrating device coupling two pendulums using multiple time scales method

• 作 者: LI Jun LIU Chu-sheng PENG Li-ping WANG Hong
• 机 构: School of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou 2
• 出 处: 中南大学学报（英文版）
• 发表日期: 2013年期
• 关键词: free vibration coupling pendulums multiple time scales method nonlinear characte

　　A model of vibrating device coupling two pendulums (VDP) which is highly nonlinear was put forward to conduct vibration analysis.Based on energy analysis, dynamic equations with cubic nonlinearities were established using Lagranges equation.In order to obtain approximate solution, multiple time scales method, one of perturbation technique, was applied.Cases of non-resonant and 1:1:2:2 internal resonant were discussed.In the non-resonant case, the validity of multiple time scales method is confirmed, comparing numerical results derived from fourth order Runge-Kutta method with analytical results derived from first order approximate expression.In the 1:1:2:2 intemal resonant case, modal amplitudes of Aa1 and Ab2 increase, respectively, from 0.38 to 0.63 and from 0.19 to 0.32, while the corresponding frequencies have an increase of almost 1.6 times with changes of initial conditions, indicating the existence of typical nonlinear phenomenon.In addition, the chaotic motion is found under this condition.