模态数量对薄壁短圆柱壳振动响应分析的影响

摘要

采用振型叠加法研究薄壁短圆柱壳受谐波激励的振动响应分析时模态截断数量的影响，且考虑简支-简支、固支-固支和固支-自由三种约束条件。首先基于Love壳体理论建立薄壁短圆柱壳的动力学模型。然后，给出采用振型叠加法进行薄壁短圆柱壳受径向谐波激励时的振动响应求解方法。在三种不同约束条件下，计算采用不同模态截断数量时的稳态响应的振动幅值，对比其一致性，并与实测结果进行比较。结果表明，在这三种约束条件下计算受谐波激励薄壁短圆柱壳的振动响应，需要截取前8阶模态函数用于表征位移模式；模态数据超过8阶对响应计算的精度没有明显改善，实测振动响应结果与解析结果基本吻合。%An analysis was made to study on forced vibration response characteristics of a short thin cylindrical shell under a radial harmonic excitation force, and the modal numbers were considered for simply supported-simply supported, clamped-clamped and clamp-free boundary conditions. A dynamic model of a short thin cylindrical shell was constructed according to Love’s shell theory. Then, the dynamic equations were solved based on modal superposition method when the cylindrical shell was subject to a radial harmonic excitation force. Under three boundary conditions the vibration response results were calculated. The results show that the response amplitudes need the first eight modes to represent the displacement mode. If the modal numbers are more than eight, the precision are no more obvious improvement, and analytic results and experimental results are fundamental agreement.