薄壁圆柱壳的高阶模态振动特性研究
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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.
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.
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.
引文
1吴家龙.弹性力学.北京:高等教育出版社,2001(Wu JL.Elastic mechanics M.Beijing:Higher Education Press,2001(in Chinese))
2 Rongong J A,Tomlinson G R.Suppression of ring vibration modes of high nodal diameter using constrained layer damping methods.Smart Materials and Structures,1996,5(5):672~684
3 Wang C,Lai J C S.Prediction of natural frequencies of finite length circular cylindrical shells.Applied Acoustics,2000,59(4):385~400
4 El-Kaabazi N,Kennedy D.Calculation of natural frequencies and vibration modes of variable thickness cylindrical shells using the Wittrick-Williams algorithm.Computers&Structures,2012,104-105(4):4~12
5 El-Mously M.Fundamental natural frequencies of thin cylindrical shells:a comparative study.Journal of Sound and Vibration,2003,264(5):1167~1186
6李国臣,李永强.薄壁圆柱壳固有频率的计算.机械科学与技术,2010,9(9):1226~1229(Li G C,Li Y Q.Calculating natural frequencies of thin circular cylindrical shells.Mechanical Science and Technology,2010,9(9):1226~1229(in Chinese))
7杜长城,李映辉.功能梯度薄壁圆柱壳的自由振动.动力学与控制学报,2010,8(3):219~223(Du C C,Li Y H.Free vibration of functionally graded cylindrical thin shells.Journal of Dynamics and Control,2010,8(3):219~223(in Chinese))
8张爱国,李文达,杜敬涛等.不同边界条件正交各向异性圆柱壳结构固有振动分析.哈尔滨工程大学学报,2014,(4):420~425(Zhang A G,Li W D,Du J T,et al.Natural vibration analysis of the orthotropic cylindrical shell structure with various boundary conditions.Journal of Harbin Engineering University,2014,(4):420~425(in Chinese))
9杨毅,魏光涛,阎桂荣.圆柱壳自由振动特性分析方法研究.应用力学学报,2011,28(1):59~63,110(Yang Y,Wei G T,Yan G R.The research of vibration analysis methods for circular shell.Chinese Journal of Applied Mechanics,2011,28(1):59~63,110(in Chinese))
10陈正翔,陈维衡.圆柱壳中较高阶结构振动波的传播特性.华中理工大学学报,1997,(11):93~95(Chen ZX,Zhang W H.Dispersion characteristics of higher order structural vibration waves in cylindrical shells.Journal of Huazhong University of Science and Technology,1997,(11):93~95(in Chinese))
11韩清凯,王宇,李学军.旋转薄壁圆柱壳的高节径振动特性以及篦齿结构的影响.中国科学:物理学、力学、天文学,2013,43(4):436~458(Han Q K,Wang Y,Li XJ.High nodal diameter vibration characteristics of rotating shell and the effects of its sealing teeth.Scientia Sinica Physica,Mechanica&Astronomica,2013,43(4):436~458(in Chinese))
12李晖,孙伟,许卓等.基于激光旋转扫描的约束态薄壁圆柱壳模态振型测试新方法.振动与冲击,2014,33(16):155~159(Li H,Sun W,Xu Z,et al.Experimental method of laser rotating scanning to measure mode shapes of constrained thin cylindrical shell.Journal of Vibration and Shock,2014,33(16):155~159(in Chinese))
13陈丽华,孙玥,张伟.三阶剪切变形板的振动特性研究.动力学与控制学报,2014,12(1):50~55(Chen L H,Sun Y,Zhang W.Study on vibration characteristic of third order shear deformation theory of plate.Journal of Dynamics and Control,2014,12(1):50~55(in Chinese))
14 Soedel W.Vibrations of shells and plates.CRC Press,2004
15洪杰,郭宝亭,朱梓根.高速转动壳体行波振动实验研究.航空动力学,1998,13(4):390~394(Hong J,Guo B T,Zhu Z G.Experimental investigation on travelling wave vibration of high-speed rotating shell.Journal of Aerospace Power,1998,13(4):390~394(in Chinese))
2 Rongong J A,Tomlinson G R.Suppression of ring vibration modes of high nodal diameter using constrained layer damping methods.Smart Materials and Structures,1996,5(5):672~684
3 Wang C,Lai J C S.Prediction of natural frequencies of finite length circular cylindrical shells.Applied Acoustics,2000,59(4):385~400
4 El-Kaabazi N,Kennedy D.Calculation of natural frequencies and vibration modes of variable thickness cylindrical shells using the Wittrick-Williams algorithm.Computers&Structures,2012,104-105(4):4~12
5 El-Mously M.Fundamental natural frequencies of thin cylindrical shells:a comparative study.Journal of Sound and Vibration,2003,264(5):1167~1186
6李国臣,李永强.薄壁圆柱壳固有频率的计算.机械科学与技术,2010,9(9):1226~1229(Li G C,Li Y Q.Calculating natural frequencies of thin circular cylindrical shells.Mechanical Science and Technology,2010,9(9):1226~1229(in Chinese))
7杜长城,李映辉.功能梯度薄壁圆柱壳的自由振动.动力学与控制学报,2010,8(3):219~223(Du C C,Li Y H.Free vibration of functionally graded cylindrical thin shells.Journal of Dynamics and Control,2010,8(3):219~223(in Chinese))
8张爱国,李文达,杜敬涛等.不同边界条件正交各向异性圆柱壳结构固有振动分析.哈尔滨工程大学学报,2014,(4):420~425(Zhang A G,Li W D,Du J T,et al.Natural vibration analysis of the orthotropic cylindrical shell structure with various boundary conditions.Journal of Harbin Engineering University,2014,(4):420~425(in Chinese))
9杨毅,魏光涛,阎桂荣.圆柱壳自由振动特性分析方法研究.应用力学学报,2011,28(1):59~63,110(Yang Y,Wei G T,Yan G R.The research of vibration analysis methods for circular shell.Chinese Journal of Applied Mechanics,2011,28(1):59~63,110(in Chinese))
10陈正翔,陈维衡.圆柱壳中较高阶结构振动波的传播特性.华中理工大学学报,1997,(11):93~95(Chen ZX,Zhang W H.Dispersion characteristics of higher order structural vibration waves in cylindrical shells.Journal of Huazhong University of Science and Technology,1997,(11):93~95(in Chinese))
11韩清凯,王宇,李学军.旋转薄壁圆柱壳的高节径振动特性以及篦齿结构的影响.中国科学:物理学、力学、天文学,2013,43(4):436~458(Han Q K,Wang Y,Li XJ.High nodal diameter vibration characteristics of rotating shell and the effects of its sealing teeth.Scientia Sinica Physica,Mechanica&Astronomica,2013,43(4):436~458(in Chinese))
12李晖,孙伟,许卓等.基于激光旋转扫描的约束态薄壁圆柱壳模态振型测试新方法.振动与冲击,2014,33(16):155~159(Li H,Sun W,Xu Z,et al.Experimental method of laser rotating scanning to measure mode shapes of constrained thin cylindrical shell.Journal of Vibration and Shock,2014,33(16):155~159(in Chinese))
13陈丽华,孙玥,张伟.三阶剪切变形板的振动特性研究.动力学与控制学报,2014,12(1):50~55(Chen L H,Sun Y,Zhang W.Study on vibration characteristic of third order shear deformation theory of plate.Journal of Dynamics and Control,2014,12(1):50~55(in Chinese))
14 Soedel W.Vibrations of shells and plates.CRC Press,2004
15洪杰,郭宝亭,朱梓根.高速转动壳体行波振动实验研究.航空动力学,1998,13(4):390~394(Hong J,Guo B T,Zhu Z G.Experimental investigation on travelling wave vibration of high-speed rotating shell.Journal of Aerospace Power,1998,13(4):390~394(in Chinese))