矩形薄板的刚柔耦合动力学系统的建模理论研究

Study on Dynamic Modeling Theory of Rigid Flexible Coupling Systems for Flexible Rectangular Plate

以由中心刚体与柔性板构成的刚柔耦合系统为对象,研究了零次近似模型和耦合模型在动力学方程以及实际计算中表现出来的差异。首先,从连续介质理论出发,在变形位移中,计及了在结构动力学中被忽略的变形位移的附加耦合项,建立了由中心刚体与柔性板构成的刚柔耦合系统的一次近似动力学模型。用一致质量有限元法对柔性板进行离散,基于Jourdain速度变分原理推导出大范围运动为自由的柔性板刚柔耦合动力学连续变分方程。通过数值仿真研究中心刚体和柔性板的大范围运动和变形运动的规律,揭示刚柔耦合动力学性质。通过数值对比,指出了零次近似模型的局限性。

Based on the continuum medium mechanics, the quadratic term of partial derivative of deformation displacement with respect to the spatial position was kept in the related equation. The coupling terms of deformation motion were deduced. Two models were presented： zero order coupling model and first order coupling model. The finite element method was used for the system discretization and the coupling dy- namic equations of flexible plate attached to a central rigid body were obtained by using Jourdain＇s velocity variation principle. The angular velocity and the tip deformation of the pendulum were calculated. The difference of the dynamic property between zero order and coupling model was revealed.