薄壁圆柱壳的高阶模态振动特性研究
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Study on vibration characteristics of high-order modal for a thin cylindrical shell
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国家自然科学基金资助项目(51105187)、辽宁科技大学青年基金资助项目(2014QN13)

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    摘要:

    采用解析法研究了不同边界条件下薄壁圆柱壳的高阶模态振动特性.首先基于Love壳体理论,在简支简支、固支固支和固支自由三种边界条件下,通过伽辽金法建立了动力学模型,对模态特性进行求解,得到了高阶固有频率和三维模态振型,并通过文献和有限元法进行了比较.算例结果表明,两端简支边界条件下采用解析法得到的固有频率误差值不超过2%,当周向波数较小时固有频率先减小后增加,在高阶时的固有频率逐渐升高,当轴向半波数增加时固有频率明显增大,通过解析法、文献和有限元法得到的三维模态振型相吻合.

    Abstract:

    The vibration characteristics on a highorder modal of a thin cylindrical shell is studied in this paper by analytical method under different boundary conditions. Firstly, the shell dynamics model is established by Galerkin′s method based on Love′s shell theory under simply supportedsimply supported, clampedclamped and clampedfree boundary conditions. Secondly, the modal characteristics are solved, and the highorder natural frequencies as well as threedimensional mode shapes are obtained. Finally, the results are compared with the data from the related literature and finite element method. The results show that the error values of natural frequencies using analytical method are less than 2% for the shell under simply supported boundary condition at both ends. The natural frequency increases after the first decrease when circumferential wave numbers are small, while it increases gradually when circumferential wave numbers are higher, but the natural frequencies increase significantly when axial halfwave numbers rise. Moreover, the threedimensional modal shapes obtained from the analytical method, related literature and finite element method are coincident.

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王宇,罗忠,李昌,刘健.薄壁圆柱壳的高阶模态振动特性研究[J].动力学与控制学报,2016,14(2):131~137; Wang Yu, Luo Zhong, Li Chang, Liu Jian. Study on vibration characteristics of high-order modal for a thin cylindrical shell[J]. Journal of Dynamics and Control,2016,14(2):131-137.

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  • 收稿日期:2014-12-04
  • 最后修改日期:2014-12-27
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  • 在线发布日期: 2016-04-11
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