基于微分求积法分析旋转圆板的横向振动

基于微分求积法，分析了旋转圆板的横向振动和稳定性问题。从平面应力问题和Kirchhoff薄板理论出发，得到了在沿径向线性分布的离心惯性力作用下均质等厚度旋转圆板的轴对称中面内力，建立了极坐标下板的轴对称运动微分方程。对变系数的运动微分方程，采用微分求积法离散方程和边界条件，分析了周边固支、简支（沿径向不可移）和周边完全自由三种边界条件下旋转圆板的前两阶复频率的实部和虚部随角速度的变化情况，并得到其失稳类型以及相应的临界速度。

Transverse Vibration of Spinning Circular Plate Based onthe Differential Quadrature Method

Based on the differential quadrature method, the transverse vibration and stability concerning of spinning circular plate is investigated. According to the plane stress problem and Kirchhoff’s thin plate theory, the middle internal forces of axisymmetric spinning circular plate with homogeneity and constant thickness are obtained under the action of linearly distributed normal inertial force along the radial direction of the spinning circular plate, and the differential equation of motion with variable coefficients for the axisymmetric spinning circular plate is established in the form of polar coordinates. The differential quadrature method is employed to discretize the differential equation with variable coefficients and corresponding to some bound-ary conditions. Through numerical calculation for spinning circular plate with simply supported edge, clamped edge (non-radial displacement at the external boundary) and completely free edge, the real parts and imaginary parts of the first two order complex frequency versus the angular speed are analyzed, and their sta-bility types and corresponding to critical angular speed are obtained respectively.