含环向表面裂纹充液圆柱壳的耦合振动特性分析

PDF(981 KB)

振动与冲击 ›› 2018, Vol. 37 ›› Issue (23) : 71-77.

论文

金超超 1,2,3 ，朱翔 1,2,3，李天匀 1,2,3，方敏 1,2,3

作者信息 +

Coupled vibration feature analysis for a fluid-filled cylindrical shell with a circumferential surface crack

JIN Chaochao1,2,3,ZHU Xiang1,2,3,LI Tianyun1,2,3,FANG Min1,2,3

Author information +

文章历史 +

摘要

对含环向表面裂纹有限长充液圆柱壳的耦合振动特性进行了研究。通过在经典薄壳理论中引入基于断裂力学的线弹簧模型来模拟环向表面裂纹。根据理想流体在柱坐标系下的Helmholtz波动方程，通过添加流体载荷项建立了圆柱壳的耦合振动控制方程，采用波传播法描述耦合系统的振动。采用优化迭代的方法有效地计算对应特定固有频率的轴向波数，在此基础上迭代计算满足特定边界条件和裂纹位置连续性条件的固有频率值。为验证本文方法的准确性，将计算模型分别退化为真空中完善圆柱壳，真空中裂纹圆柱壳，充液完善圆柱壳，三种情况与文献及有限元方法结果进行对比，验证了本文方法的准确性。讨论了裂纹深度和裂纹位置参数对圆柱壳固有频率改变的影响。

Abstract

The coupled vibration characteristics of a fluid-filled finite-length cylindrical shell with a circumferential surface crack were studied.Introducing a line spring model to simulate the circumferential surface crack in the classical thin shell theory,according to ideal fluid’s Helmholtz wave equation in cylindrical coordinates,applying the acoustic load of fluid on the shell based on the wave propagation method,and then the fluid-filled cylindrical shell’s coupled vibration control equation was built.The relationship between natural frequencies and axial wave-number of the cylindrical shell was solved with an optimal iterative method.Furthermore,the cylindrical shell’s natural frequencies were iteratively computed to satisfy the specific boundary condition and the continuity condition of crack position.The computation model was degenerated into 3 cases of a perfect cylindrical shell in vacuum,a cracked one in vacuum and a perfect fluid-filled one.The computation results of 3 cases were compared with those published in literature and calculated using the FEM,respectively.All results agreed well with each other to verify the correctness of the proposed method.Finally,the effects of crack depth and its position on the cylindrical shell’s natural frequencies were examined.

导出引用

金超超 1,2,3,朱翔 1,2,3，李天匀 1,2,3，方敏 1,2,3. 含环向表面裂纹充液圆柱壳的耦合振动特性分析[J]. 振动与冲击, 2018, 37(23): 71-77

JIN Chaochao1,2,3,ZHU Xiang1,2,3,LI Tianyun1,2,3,FANG Min1,2,3. Coupled vibration feature analysis for a fluid-filled cylindrical shell with a circumferential surface crack[J]. Journal of Vibration and Shock, 2018, 37(23): 71-77

参考文献

[1] Zhang XM, Liu GR, Lam KY. Vibration analysis of thin cylindrical shells using wave propagation approach [J]. Journal of Sound & Vibration, 2001, 239(3):397-403.
[2] Zhang XM, Liu GR, Lam KY. Coupled vibration analysis of fluid-filled cylindrical shells using the wave propagation approach [J]. Applied Acoustics, 2001, 62(3):229-243.
[3] 刘敬喜，李天匀，刘土光，等. 弹性介质中充液圆柱壳的轴对称振动分析[J]. 振动与冲击，2005, 24(4):78-80.
LIU Jing-xi, LI Tian-yun, LIU Tu-guang, et al. Analysis of axisymmetric vibration of cylindrical shells in elastic medium [J]. Journal of vibration and shock, 2005, 24(4): 78-80.
[4] Zafar, Iqbal, Muhammad, Nawaz, Naeem, Nazra, et al. Vibration characteristics of FGM circular cylindrical shells filled with fluid using wave propagation approach [J]. Applied Mathematics and Mechanics, 2009, 30(11):1393-1404.
[5] Amabili M. Free Vibration of a fluid-filled circular cylindrical shell with lumped masses attached, using the receptance method [J]. Shock & Vibration, 2013, 3(3):159-167.
[6] 郭文杰，李天匀，朱翔，等. 计及自由液面影响的水下有限深度圆柱壳自由振动分析[J]. 振动与冲击，2017, 2017(10): 1-6.
GUO Wen-jie, Tian-yun, ZHU Xiang, et al. Free vibration of a submerged cylindrical shell considering the effect of free surface in finite depth [J]. Journal of vibration and shock, 2017, 2017(10):1-6.
[7] Rice J R, Levy N. The Part-Through Surface Crack in an Elastic Plate [J]. Journal of Applied Mechanics, 1972, 39(1):185-194.
[8] Nikpour K. Diagnosis of axisymmetric cracks in orthotropic cylindrical shells by vibration measurement [J]. Composites Science & Technology, 1990, 39(1):45-61.
[9] 彭凡，彭献. 简支梁裂纹位置识别的一种简单方法[J]. 振动与冲击，2001, 20(4):75-76.
PENG Fan, PENG Xian. A simple method for identifying crack position of simple-supported beam [J]. Journal of vibration and shock, 2001, 20(4): 75-76.
[10] Zhu X, Li TY, Zhao Y, Yan J. Vibrational power flow analysis of thin cylindrical shell with a circumferential surface crack [J]. Journal of Sound & Vibration, 2007, 302(1–2):332-349.
[11] Li TY, Zhu X, Zhao Y, Hu XF. The wave propagation and vibrational energy flow characteristics of a plate with a part-through surface crack [J]. International Journal of Engineering Science, 2009, 47(10):1025-1037.
[12] Yin T, Li DQ, Zhu HP. A new solution method for vibration analysis of circular cylindrical thin shells with a circumferential surface crack [J]. Advanced Materials Research, 2013, 640(1):1003-1009.
[13] Yin T, Lam HF. Dynamic analysis of finite-length circular cylindrical shells with a circumferential surface crack [J]. J Eng Mech, 2013, 139(10):1419-1434.
[14] 罗志钢，蒋占四，王衍学，等. 基于无网格法梁结构多裂纹定量识别[J]. 振动与冲击，2016, 35(13):206-211.
LUO Zhi-gang, JIANG Zhan-si, WANG Yan-xue, et al. Multi-crack detection of beam structures based on meshless method [J]. Journal of vibration and shock, 2016, 35(13):206-211.
[15] Flügge W. Stresses in Shells [D]. Berlin Heidelberg: Springer, 1973.
[16] 陈正翔, 江松青, 张维衡. 圆柱壳中结构振动波的传播特性[J]. 振动工程学报, 1998(4):450-456.
CHEN Zheng-xiang, JIANG Song-qing, ZHANG Wei-heng. Propagation characteristics of structural vibration wave in cylindrical shell [J]. Journal of Vibration Engineering, 1998(4):450-456.