高速旋转薄壁圆柱壳的行波共振特性研究

摘要

基于传递矩阵法研究了不同边界条件下高速旋转薄壁圆柱壳的行波共振特性。首先，基于 Love 壳体理论，考虑离心力、科氏力和惯性力的影响，建立了旋转态薄壁圆柱壳的振动微分方程；然后，引入传递矩阵方法，根据壳体子段间的状态向量表达式，推导了结构的整体传递矩阵；最后，通过高精度的精细积分法进行求解，得到了两端简支、两端固支和固支－自由边界条件下的共振特性。算例结果表明，传递矩阵方法适合于求解高速旋转薄壁圆柱壳的行波共振特性，在三种边界条件下以周向模态的振动为主；在工作转速和1倍频激振力作用下，共振裕度小于10％的共振转速点仅有一个，而在其他倍频激振下的共振转速点不在安全裕值范围内。%The traveling wave resonance characteristics of a high-speed rotating thin cylindrical shell were studied under different boundary conditions based on the transfer matrix method.Firstly,the vibration differential equations of the rotating thin cylindrical shell were set up based on Love's shell theory considering the effects of centrifugal forces,coriolis forces and inertial forces.Secondly,with the state vector expression between sub-segments,the transfer matrix method was introduced to derive the overall transfer matrix of the structure.Finally,its resonance characteristics were solved with the high-precise integration method under simply supported-simply supported, clamped-clamped and clamped-free boundary conditions.The example's results showed that the transfer matrix method is suitable for solving the resonance characteristics of the high-speed rotating thin cylindrical shell,and the vibration modes in circumferential direction are the main contributors to the resonance of the shell under three boundary conditions;there is only one resonance rotating speed point when the resonance margin is less than 10% under the operating rotating speed and the first octave excitation,but the resonance rotating speed points under other octave excitations are not within the safe margin range.