In order to study on nonlinear vibration of flexible manipulator, a mathematical model of mechanical system considering damping, material nonlinearity, temperature variation and axial excitation was established using the Garlerkin method. Furthermore, the adequate and essential conditions for homoclinic orbits, hetroclinic orbits and period orbits were obtained by Hamilton functions of the system, and the corresponding specific analytic expressions of different orbits were deduced. Based on the multiple scales method for nonlinear vibration analysis, the first approximation solutions and corresponding to steady state solutions of the 3 super-harmonic resonances were studied. The relations between different parameters were revealed clearly. Numerical analysis results show that material nonlinearity and temperature variation are critical factors influencing the vibration, which should not be neglected. In some conditions, the movement such as chaotic motion can be found in the system. In order to control the flexible manipulator effectively, parameters should be designed correctly to avoid the chaotic movement.
Yun Chao, Cui Yihui, Wang Wei, Tang Qing.Super-harmonic resonance and complex movement analysis of flexible manipulator in temperature field[J] JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2009,V35(2): 236-240