Sub-harmonic resonance and complex movement analysis of flexible manipulator in temperature field

In order to study on nonlinear vibration of flexible manipulator, a mathematical model of mechanical system considering damping, material nonlinearity and temperature variation is established using the Garlerkin method. Furthermore, the adequate and essential conditions for homoclinic orbits, hetroclinic orbits and period orbits are obtained. Based on multiple scales method for nonlinear vibration analysis, the first approximation solutions and corresponding to steady state solutions of the 1/3 subharmonic resonances are studied. Numerical analysis results show that the effect of material nonlinearity and temperature variation cannot be neglected. In some conditions, the flexible movement such as chaotic motion can be found in the system.