Forced vibration steady-state response of thin-walled cylindrical shell on elastic foundation based on Donnell-Mushtari theory
YANG Yongbao1,WEI Yintao1,LI Xuebing1,ZHANG Xinyue2
1.State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China;
2. College of Vehicles and Energy, Yanshan University, Qinhuangdao 066004, China
Based on the DonnellMushtari shell theory, exact solutions to the free vibration frequency of a thinwalled cylindrical shell subjected to radial prepressure with elastic foundations at both ends were presented, and there is little difference between the results by this method and those available in the literature. With the free vibration frequency and modal shapes of the thinwalled cylindrical shell obtained by using this method, the formulas for forced vibration steadystate responses were developed. The influence of modal numbers and damping factor on steadystate responses of the thinwalled cylindrical shell has also been investigated. The results and conclusions of numerical examples can provide references for engineering applications.
杨永宝,危银涛1,李雪冰1,张新月2. 基于Donnell-Mushtari理论的弹性基础薄壁圆柱壳的稳态响应研究[J]. 振动与冲击, 2018, 37(6): 21-27.
YANG Yongbao1,WEI Yintao1,LI Xuebing1,ZHANG Xinyue2. Forced vibration steady-state response of thin-walled cylindrical shell on elastic foundation based on Donnell-Mushtari theory. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(6): 21-27.
[1]Saito T, Endo M. Vibration of finite length, rotatingcylindrical shells[J]. Journal of Sound and Vibration, 1986, 107(1): 17-28.
[2]Smith B L, Vronay D F. Free vibration of circular cylindrical shells of finite length[J]. AIAA Journal, 1970, 8(3): 601-603.
[3]Zhang X M, Liu G R, Lam K Y. Vibration analysis of thin cylindrical shells using wave propagation approach[J]. Journal of Sound and Vibration, 2001, 239(3): 397-403.
[4]Ip K H, Chan W K, Tse P C, et al. Vibration analysis of orthotropic thin cylindrical shells with free ends by the Rayleigh-Ritz method[J]. Journal of sound and vibration, 1996, 195(1): 117-135.
[5]Xuebin L. Study on free vibration analysis of circularcylindrical shells using wave propagation[J]. Journal of Sound and Vibration, 2008, 311(3): 667-682.
[6]Dym C L. Some new results for the vibrations ofcircular cylinders[J]. Journal of sound and Vibration, 1973, 29(2): 189-205.
[7]Soedel W. Simplified equations and solutions for the vibration of orthotropic cylindrical shells[J]. Journal of Sound and Vibration, 1983, 87(4): 555-566.
[8] Karczub D G. Expressions for direct evaluation of wave number in cylindrical shell vibration studies using the Flügge equations of motion [J]. The Journal of the Acoustical Society of America, 2006, 119(6): 3553-3557.
[9] Leissa A W. Vibration of shells[M]. New York: Acoustical Society of America, 1993.
[10] Sheng J. The response of a thin cylindrical shell to transient surface loading [J]. AIAA Journal, 1965, 3(4): 701-709.
[11] Warburton G B. Harmonic response of cylindrical shells [J]. Journal of Engineering for Industry, 1974, 96(3): 994-999.
[12]Christoforou A P, Swanson S R. Analysis of simply-supported orthotropic cylindrical shells subject to lateral impact loads [J]. Journal of Applied Mechanics, 1990, 57(2): 376-382.
[13] Jafari A A, Khalili S M R, Azarafza R. Transient dynamic response of composite circular cylindrical shells under radial impulse load and axial compressive loads [J]. Thin-Walled Structures, 2005, 43(11): 1763-1786.
[14] 马旭, 杜敬涛, 杨铁军, 等. 基于波传播方法的边界条件对圆柱壳振动特性的影响分析[J]. 振动工程学报, 2009, 22(6): 608-613.
Ma Xu, Du Jingtao, Yang Tiejun, et al. Analysis of influence of boundary conditions on cylindrical shell dynamics based on wave propagation approach [J]. Journal of vibration Engineering, 2009, 22(6): 608-613.
[15] 王宇, 罗忠. 薄壁圆柱壳构件受迫振动的响应特征研究[J]. 振动与冲击, 2015, 34(7): 103-108.
Wang Yu, Luo Zhong. Forced vibration response characteristics of thin cylindrical shell [J]. Journal of vibration and shock, 2015, 34(7): 103-108.
[16]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.
[17]李学斌. 圆柱壳稳态动力响应分析[J]. 舰船科学技术, 2000 (6): 1-5.
[18]左言言, 宫镇. 圆柱壳受激振动的分析研究[J]. 农业机械学报, 1998, 29(1): 88-93.
[19] 陈正翔, 江松青. 圆柱壳中结构振动波的传播特性[J]. 振动工程学报, 1998, 11(4): 450-456.
Chen Zhengxiang, Jiang Songqing. Dispersion characteristics of structure vibration waves in cylindrical shells [J]. Journal of vibration Engineering, 1998, 11(4): 450-456.
[20] J.M. Santiago, H.L. Wisniewski, Convergence of finite element frequency prediction for a thin walled cylinder [J]. Computers and Structures 32 (3/4) (1989) 745–759.