|
|
|
| Free vibration analysis for cylindrical shells with variable thickness based on precise transfer matrix method |
| JIANG Chenban1, WANG Xianzhong2,3, ZUO Yingying2,3 |
1.China Ship Scientific Research Center, Wuxi 214082, China;
2.Key Laboratory of High Performance Ship Technology of Ministry of Education, Wuhan University of Technology, Wuhan 430063, China;
3.School of Transportation, Wuhan University of Technology, Wuhan 430063, China |
|
|
|
|
Abstract Combining the precise integration and the transfer matrix method, free vibration of a cylindrical shell with variable thickness was calculated and analyzed.Based on basic equations of cylinder shells, first order homogeneous partial differential equations for a cylinder shell with variable thickness’s displacement and internal force vectors were derived to solve their field transfer matrices using the precise integration.The cylinder shell’s total transfer equation was assembled with the field transfer matrices obtained with precise integration.According to boundary conditions, natural frequencies of the cylindrical shell with variable thickness were calculated by solving determinant of coefficient matrix of the total transfer equation.The calculation results using the proposed method were compared with those using the finite element method to verify the correctness and effectiveness of the proposed method.Meanwhile, effect laws of boundary condition, thickness varying form, thickness variation coefficient and ratio of the cylinder shell’s length to diameter on its free vibration were explored.
|
|
Received: 06 July 2018
Published: 28 January 2020
|
|
|
|
[1] Rayleigh J W S B, Lindsay R B. The theory of sound[M]. America: Dover Publications, 1945.
[2] Xie Kun, Chen Mei-xia, Zhang Lei, et al. Free and forced vibration analysis of non-uniformly supported cylindrical shells through wave based method[J]. International Journal of Mechanical Sciences, 2017, 128-129:512-526.
[3] Yamada G, Irie T, Tagawa Y. Free vibration of non-circular cylindrical shells with variable circumferential profile[J]. Journal of Sound & Vibration, 1984, 95(1):117-126.
[4] 李文达, 杜敬涛, 杨铁军, 等. 基于改进傅里叶级数方法的旋转功能梯度圆柱壳振动特性分析[J]. 哈尔滨工程大学学报, 2016, 37(3):388-393.
Li Wen-da, Du Jing-tao, Yang Tie-jun, et al. Vibration characteristics analysis of the rotating functionally graded cylindrical shell structure using an improved Fourier series method[J]. Journal of Harbin Engineering University, 2016, 37(3):388-393.
[5] 陈旭东, 叶康生. 中厚圆柱壳自由振动的动力刚度法分析[J]. 工程力学, 2016, 33(9):40-48.
Chen Xu-dong, Ye Kang-sheng. Analysis of free vibration of moderately thick circular cylindrical shells using the dynamic stiffness method [J]. Engineering Mechanics, 2016, 33(9):40-48.
[6] Qu Ye-gao, Hua Hong-xing, Meng Guang. A domain decomposition approach for vibration analysis of isotropic and composite cylindrical shells with arbitrary boundaries[J]. Composite Structures, 2013, 95:307-321.
[7] Zhang L, Xiang Y. Exact solutions for vibration of stepped circular cylindrical shells[J]. Journal of Sound & Vibration, 2007, 299(4–5):948-964.
[8] 曹雷, 马运义, 黄玉盈. 环肋加强变厚度圆柱壳的自由振动[J]. 华中科技大学学报(城市科学版), 2007, 24(2):63-66.
Cao Lei, Ma Yun-yi, Huang Yu-ying. Free vibration of ring-stiffened circular cylindrical shell with variable thickness[J]. Journal of Huazhong University of Science and Technology(Urban Science Edition), 2007, 24(2):63-66.
[9] Duan W H, Koh C G. Axisymmetric transverse vibrations of circular cylindrical shells with variable thickness[J]. Journal of Sound & Vibration, 2008, 317(3–5):1035-1041.
[10] El-Kaabazi N, Kennedy D. Calculation of natural frequencies and vibration modes of variable thickness cylindrical shells using the Wittrick–Williams algorithm[J]. Computers & Structures, 2012, s 104–105(4):4-12.
[11] Qu Ye-gao, Chen Yong, Long Xin-hua, et al. Free and forced vibration analysis of uniform and stepped circular cylindrical shells using a domain decomposition method[J]. Applied Acoustics, 2013, 74(3):425-439.
[12] Poultangari R, Nikkhahbahrami M. Free and forced vibration analysis of stepped circular cylindrical shells with several intermediate supports using an extended wave method; a Generalized Approach[J]. Lat.am.j.solids Struct, 2016, 13(11):2027-2058.
[13] Tang Dong, Yao Xiong-liang, Wu Guo-xun, et al. Free and forced vibration analysis of multi-stepped circular cylindrical shells with arbitrary boundary conditions by the method of reverberation-ray matrix[J]. Thin-Walled Structures, 2017, 116:154-168.
[14] Wang Xian-zhong, Wu Wei-guo, Yao Xiong-liang. Structural and acoustic response of a finite stiffened conical shell[J]. Acta Machanica Solida Sinica, 2015, 28(2):200-209.
[15] Wang Xian-zhong, Wu Wei-guo. Dynamic modeling and vibration characteristics analysis of submerged stiffened combined shells[J]. Ocean Engineering, 2016, 127:226-235.
[16] 王献忠. 环肋旋转壳声振特性分析的半数值方法[J]. 振动工程学报, 2015, 28(5):793-799.
Wang Xian-zhong. A semi-numerical method for predicting the vib-acoustic problem of stiffened shells of revolution[J]. Journal of Vibration Engineering, 2015, 28(5):793-799.
[17] 王祖华, 彭旭. 短粗环肋圆柱壳振动特性分析的传递矩阵法[C]. 船舶水下噪声学术讨论会. 2009:129-135.
Wang Zu-hua, Peng xu. Vibration characteristics analysis of submerged ring-stiffened cylindrical shells with relatively less span and larger diameter with transfer matrix method[C]. Seminar on Marine Underwater Noise. 2009:129-135.
[18] 谭述君, 高强, 钟万勰. Duhamel项的精细积分方法在非线性微分方程数值求解中的应用[J]. 计算力学学报, 2010, 27(5):752-758.
Tan Shu-jun, Gao Qiang, Zhong Wan-xie. Application of Duhamel term’s precise integration method in solving nonlinear differential equations[J]. Chinese Journal of Computational Mechanics, 2010, 27(5):752-758.
[19] 钟万勰. 结构动力方程的精细时程积分法[J]. 大连理工大学学报, 1994(2):131-136.
Zhong Wan-xie. On precise time-integration method for structural dynamics[J]. Journal of Dalian University of Technology, 1994(2):131-136.
|
|
|
|
