定轴转动与基础激励下梁的非线性动力学

采用Kane方程，建立了含耦合的几何及惯性非线性项的定轴转动与轴向基础激励联合作用下柔性梁的非线性动力学控制方程组，该方程组不仅包含二次及三次非线性项，而且体现了参数激励与外激励的联合作用。运用多尺度法，研究了匀转速，顺臂安装下悬臂梁的一阶模态主参激共振与外激励1/2次亚谐共振同时作用时梁的一阶近似稳态响应。结果表明，梁的一阶模态幅频特性将受到转速，旋转半径和激励幅值等参数变化的显著影响。

Nonlinear Dynamics of Flexible Beams under Rotation and Axially Parametric Joint Excitation

Nonlinear dynamic modeling of flexible beams under rotation and axially parametric joint excitation is presented in this paper. The equations of motion of beam, which includes not only quadratic and cubic nonlinearities but also parametric and forced excitations are derived using Kane's equation. For a case study of a flexible cantilever beam, multiple metrics method is used to solve the nonlinear differential equations and derive the nonlinear modulation equations for the combination of the principal parametric and 1/2 subharmonic resonance of the first mode. The results show that the rotating speed, whirling radius and excitation amplitude on the beam play important roles in the planar response of the first mode of the beam.