带有弹簧－质量－圆柱壳耦合结构自由振动分析

摘要

采用子结构导纳法研究了简支边界条件下带有多根弹簧－集中质量－圆柱壳耦合结构的自由振动。根据已有结果，通过求解多根弹簧等效刚度的推导思路，采用柔度法得到各子结构矩阵元素的柔度系数，进而求得集中质量带有多根弹簧的圆柱壳耦合结构自振频率及模态理论公式，并与已有文献结果作对比，证明了理论推导的正确性。应用理论方法进一步求解了集中质量带有三根弹簧圆柱壳耦合结构的自振频率及振型，并与建立的 ANSYS 有限元模型分析结果对比，二者结果的误差可忽略不计，再次验证所提出理论的合理性及正确性。%The free vibration of a spring-mass-cylindrical shell coupled structure under simply supported boundary condition was investigated with the substructure receptance method.Through deriving the equivalent stiffness of several springs,the compliance coefficients of matrix elements of sub-structures were derived with the compliance method. Theoretical formulas for the natural frequencies and modes of the coupled structure via the receptance method,they were compared with those in other reference to verify the validity of the theoretical derivation here.The numerical results for natural frequencies and modal shapes of a three springs-lumped mass-sylinder shell coupled structure obtained with the proposed method were compared with those using the finite element software ANSYS to verify the reasonability and correctness of the theory presented here.