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| Modal characteristics analysis of cylindrical shells based on beam functions-Ritz method |
Gang-hui XU( ),Chang-sheng ZHU*() |
| College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China |
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Abstract The calculation accuracy of a single beam function is insufficient, when the function is used as an admissible function of the axial modal shape of cylindrical shells, and the results obtained based on different thin shell theories are difficult to compare directly. The beam function was combined with the Ritz method to establish a unified method including different thin shell theories for analyzing the modal characteristics of cylindrical shells. When the number of the beam function terms was set to one, the beam functions-Ritz method degenerated to the single beam function method, i.e., the single beam function method was a special case of the beam functions-Ritz method. By comparing with the finite element simulation and the existing literature data, the disagreement in the existing literature on whether the beam function is suitable for simulating the clamped or free boundary conditions of cylindrical shells was clarified. The effects of length-to-radius ratio and thickness-to-radius ratio on the modal frequencies of cylindrical shells under different boundary conditions and the corresponding theoretical calculation accuracy were studied, and then the applicable scope of different thin shell theories was summarized. Four thin shell theories were considered, including the Donnell, Reissner, Sanders and Love theories. Results show that the beam functions-Ritz method can effectively improve the calculation accuracy of the single beam function method, and the calculation accuracy of Donnell theory was obviously lower than that of the other three theories.
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Received: 11 November 2022
Published: 16 October 2023
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| Fund: 国家自然科学基金资助项目(51975516)；重点基础研究项目(2020-ZD-232-00) |
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Corresponding Authors:
Chang-sheng ZHU
E-mail: gh_xu@zju.edu.cn;zhu_zhang@zju.edu.cn
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基于梁函数-Ritz法的圆柱壳模态特性分析
单项梁函数作为圆柱壳轴向振型容许函数时计算精度不足，基于不同薄壳理论所得研究结果难以直接对比，为此将梁函数与Ritz法相结合，建立包含不同薄壳理论的统一方法，用于分析圆柱壳模态特性. 当梁函数项数取1时，梁函数-Ritz法退化为单项梁函数法，即单项梁函数法是梁函数-Ritz法的特例. 通过与有限元仿真及现有文献数据的对比，澄清现有文献在梁函数是否适用于模拟圆柱壳固支或自由边界条件上存在的分歧. 在不同边界条件下，总结长径比与厚径比对圆柱壳模态频率及理论计算精度的影响规律，得出不同薄壳理论的适用范围. 考虑的薄壳理论包括Donnell、Reissner、Sanders及Love理论. 结果表明，梁函数-Ritz法可以有效提升单项梁函数法的计算精度；Donnell理论的计算精度明显低于其他3种理论.
关键词：
圆柱壳,
模态,
梁函数,
容许函数,
Ritz法,
薄壳理论
|
|
| [1] |
LEISSA A W. Vibration of shells [M]. New York: Acoustical Society of America, 1993.
|
|
|
| [2] |
曹志远. 板壳振动理论[M]. 北京: 中国铁道出版社, 1989.
|
|
|
| [3] |
刘彦琦, 秦朝烨, 褚福磊 不同边界条件下旋转薄壁圆柱壳的振动特性[J]. 清华大学学报: 自然科学版, 2012, 52 (1): 5- 9
LIU Yan-qi, QIN Zhao-ye, CHU Fu-lei Vibration characteristics of rotating thin cylindrical shells for various boundary conditions[J]. Journal of Tsinghua University: Science and Technology, 2012, 52 (1): 5- 9
|
|
|
| [4] |
QU Y G, HUA H X, MENG G A domain decomposition approach for vibration analysis of isotropic and composite cylindrical shells with arbitrary boundaries[J]. Composite Structures, 2013, 95: 307- 321
doi: 10.1016/j.compstruct.2012.06.022
|
|
|
| [5] |
QIN Z Y, CHU F L, ZU J Free vibrations of cylindrical shells with arbitrary boundary conditions: a comparison study[J]. International Journal of Mechanical Sciences, 2017, 133: 91- 99
doi: 10.1016/j.ijmecsci.2017.08.012
|
|
|
| [6] |
DONG Y H, HU H Y, WANG L F Critical examination on in-plane inertias for vibration characteristics of cylindrical shells[J]. Journal of Sound and Vibration, 2021, 511: 116350
doi: 10.1016/j.jsv.2021.116350
|
|
|
| [7] |
LEE H W, KWAK M K Free vibration analysis of a circular cylindrical shell using the Rayleigh–Ritz method and comparison of different shell theories[J]. Journal of Sound and Vibration, 2015, 353: 344- 377
doi: 10.1016/j.jsv.2015.05.028
|
|
|
| [8] |
孙述鹏, 曹登庆, 初世明 转动薄壁圆柱壳行波振动响应分析[J]. 振动工程学报, 2013, 26 (3): 459- 466
SUN Shu-peng, CAO Deng-qing, CHU Shi-ming Analysis of travelling wave vibration response for thin rotating cylindrical shell[J]. Journal of Vibration Engineering, 2013, 26 (3): 459- 466
doi: 10.3969/j.issn.1004-4523.2013.03.021
|
|
|
| [9] |
罗忠, 王宇, 孙宁, 等 不同边界条件下旋转薄壁短圆柱壳的强迫振动响应计算[J]. 机械工程学报, 2015, 51 (9): 64- 72
LUO Zhong, WANG Yu, SUN Ning, et al Forced vibration response calculation of rotating short thin cylindrical shells for various boundary conditions[J]. Journal of Mechanical Engineering, 2015, 51 (9): 64- 72
doi: 10.3901/JME.2015.09.064
|
|
|
| [10] |
刘一沛, 吕凯波, 张志浩, 等 时变因素作用下薄壁筒工件车削振动特性与实验[J]. 航空动力学报, 2022, 37 (3): 600- 606
LIU Yi-pei, LV Kai-bo, ZHANG Zhi-hao, et al Vibration characteristics and experiments of thin-walled cylinders in turning process with time-varying factors[J]. Journal of Aerospace Power, 2022, 37 (3): 600- 606
|
|
|
| [11] |
DAI L, YANG T J, DU J T, et al An exact series solution for the vibration analysis of cylindrical shells with arbitrary boundary conditions[J]. Applied Acoustics, 2013, 74 (3): 440- 449
doi: 10.1016/j.apacoust.2012.09.001
|
|
|
| [12] |
JIN G Y, YE T G, SU Z. Structural vibration: a uniform accurate solution for laminated beams, plates and shells with general boundary conditions [M]. Berlin: Springer-Verlag, 2015.
|
|
|
| [13] |
张帅, 李天匀, 朱翔, 等 改进傅里叶级数法求解封口锥柱球组合壳的自由振动[J]. 振动工程学报, 2021, 34 (3): 601- 609
ZHANG Shuai, LI Tian-yun, ZHU Xiang, et al Modified Fourier series method to solve the free vibration of the coupled conical-cylindrical-spherical shell with closed ends[J]. Journal of Vibration Engineering, 2021, 34 (3): 601- 609
|
|
|
| [14] |
SONG X Y, HAN Q K, ZHAI J Y Vibration analyses of symmetrically laminated composite cylindrical shells with arbitrary boundaries conditions via Rayleigh–Ritz method[J]. Composite Structures, 2015, 134: 820- 830
doi: 10.1016/j.compstruct.2015.08.134
|
|
|
| [15] |
SUN W, ZHU M W, WANG Z Free vibration analysis of a hard-coating cantilever cylindrical shell with elastic constraints[J]. Aerospace Science and Technology, 2017, 63: 232- 244
doi: 10.1016/j.ast.2017.01.002
|
|
|
| [16] |
PELLICANO F Vibrations of circular cylindrical shells: theory and experiments[J]. Journal of Sound and Vibration, 2007, 303 (1/2): 154- 170
|
|
|
| [17] |
ZHANG Y, SONG H, YU X G, et al Modeling and analysis of forced vibration of the thin-walled cylindrical shell with arbitrary multi-ring hard coating under elastic constraint[J]. Thin-Walled Structures, 2022, 173: 109037
doi: 10.1016/j.tws.2022.109037
|
|
|
| [18] |
LI H C, PANG F Z, MIAO X H, et al Jacobi–Ritz method for free vibration analysis of uniform and stepped circular cylindrical shells with arbitrary boundary conditions: a unified formulation[J]. Computers and Mathematics with Applications, 2019, 77 (2): 427- 440
doi: 10.1016/j.camwa.2018.09.046
|
|
|
| [19] |
刘延柱, 陈立群, 陈文良. 振动力学[M]. 第3版. 北京: 高等教育出版社, 2019.
|
|
|
| [20] |
DONG Y H, HU H Y, WANG L F A comprehensive study on the coupled multi-mode vibrations of cylindrical shells[J]. Mechanical Systems and Signal Processing, 2022, 169: 108730
doi: 10.1016/j.ymssp.2021.108730
|
|
|
| [21] |
RAO C K, MIRZA S A note on vibrations of generally restrained beams[J]. Journal of Sound and Vibration, 1989, 130 (3): 453- 465
doi: 10.1016/0022-460X(89)90069-2
|
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