环状周期结构面外参激振动稳定性分析
Analysis on Out-of-Plane Parametric Vibration Stability of Ring-Shaped Periodic Structures

针对工程领域广泛应用的一类受移动载荷作用的环状周期结构, 开展了面外参激弹性振动稳定性研究．首先采用Hamilton原理在载荷随动坐标系下建立了时不变动力学模型．然后应用Galerkin方法对其进行离散, 得到常微分动力学模型, 最后通过计算特征值预测了模态特性和动力稳定性．为了验证解析结果的正确性, 应用坐标变换将模型转换至惯性坐标系下, 得到时变动力学模型, 然后采用Floquét理论计算了不稳定域．该研究提供了一种解决移动载荷参激振动问题的有效途径．
This work aims at the out-of-plane parametric elastic vibration of intensively-used ring-shaped periodic structures subjected to moving loads in engineering field. A time-invariant dynamic model was established by using Hamilton principle under the load-fixed coordinates. A set of ordinary differential equations were formulated by Galerkin method. The modal characteristics and the dynamic instability were identified by means of eigenvalue. For the purpose of verification，the model was equivalently transformed into a time-variant version under the inertial frame by introducing a transformation，and the unstable regions were calculated by Floquét theory. The research provides an efficient way to solve the problem of parametric vibration induced by moving loads