含不平衡质量弹性边界约束旋转梁结构振动特性分析

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (1) : 36-45.

论文

和飞帆，杜敬涛，赵雨皓，刘杨

作者信息 +

Vibration characteristics analysis of spinning beam structure with elastic boundary constraints, unbalanced concentrated mass and axial load

HE Feifan, DU Jingtao, ZHAO Yuhao, LIU Yang

Author information +

文章历史 +

摘要

采用改进傅里叶级数方法建立了含不平衡集中质量、轴向载荷的弹性边界约束条件Rayleigh旋转梁横向振动特性分析模型。首先列出转轴-支承系统的动能、势能矩阵方程组，再通过第二类拉格朗日方程推导出转轴系统的运动方程组，最后以改进傅里叶级数作为方程的假设形态进行计算求解。研究了转轴两端支承平动刚度、旋转刚度以及轴向载荷对转轴正反向涡动临界转速的影响，分析了转轴中存在的不平衡集中质量对转轴正反向涡动频率以及正反向临界转速的影响，探究了转轴幅频特性曲线随不平衡集中质量大小、轴向作用位置以及转轴两端支承刚度变化的特性。

Abstract

Analytical model of the transverse vibration characteristics of Rayleigh spinning beam with elastic boundary constraints including unbalanced concentrated mass and axial load is established by using the improved Fourier series method. Firstly, the kinetic energy and potential energy matrix equations of the spinning shaft-support system are listed. Secondly, the motion equations of the spinning shaft system are derived by Lagrange’s equation. Finally, Improved the Fourier series are used as the assumed form of the equations to calculate and solve. The influence of supporting translational stiffness, rotational stiffness and axial load on the critical rotational speed of the spinning shaft is studied. The influence of unbalanced lumped mass in the spinning shaft on the whirl frequency and critical rotational speed of the spinning shaft is analyzed. The characteristics of the amplitude-frequency characteristic curve of the spinning shaft as a function of the unbalanced lumped mass, the axial position and the supporting stiffness at both ends of the spinning shaft were investigated.

导出引用

和飞帆，杜敬涛，赵雨皓，刘杨. 含不平衡质量弹性边界约束旋转梁结构振动特性分析[J]. 振动与冲击, 2024, 43(1): 36-45

HE Feifan, DU Jingtao, ZHAO Yuhao, LIU Yang. Vibration characteristics analysis of spinning beam structure with elastic boundary constraints, unbalanced concentrated mass and axial load[J]. Journal of Vibration and Shock, 2024, 43(1): 36-45

参考文献

[1] Lei Y G, Lin J, He Z J, et al. A review on empirical mode decomposition in fault diagnosis of rotating machinery [J]. Mechanical Systems and Signal Processing, 2013, 35(1-2): 108-126. [2] Dimarogonas A D. Vibration of cracked structures: A state of the art review [J]. Engineering Fracture Mechanics, 1996, 55(5): 831-857. [3] 孟光. 转子动力学研究的回顾与展望[J]. 振动工程学报, 2002(01): 5-13. MENG Guang. Retrospect and prospect to research on rotordynamics [J]. Journal of Vibration Engineering, 2002(01): 5-13. [4] Xiao B, Li Y X, Shi S X, et al. Analysis of bending-torsional-axial vibration of multi-stage variable-section shaft system [J]. Results in Physics, 2022, 36: 105460. [5] Ma H, Zhao Q B, Zhao X Y, et al. Dynamic Characteristics Analysis of a Rotor-stator System under Different Rubbing Forms [J]. Applied Mathematical Modelling, 2015, 39(8): 2392-2408. [6] Mao Q B. Free Vibrations of Spinning Beams Under Nonclassical Boundary Conditions Using Adomian Modified Decomposition Method [J]. International Journal of Structural Stability & Dynamics, 2014, 14(07): 1450027-. [7] Mao Q B, Pietrzko S. Free vibration analysis of stepped beams by using Adomian decomposition method [J]. Applied Mathematics & Computation, 2010, 217(7): 3429-3441. [8] Banerjee J R, Su H. Dynamic stiffness formulation and free vibration analysis of a spinning composite beam[J]. Computers & Structures, 2006, 84(19/20): 1208-1214. [9] Pai P F, Qian X, Du X. Modeling and dynamic characteristics of spinning Rayleigh beams[J]. Chinese Journal of Theoretical & Applied Mechanics, 2013, 68(3): 291-303. [10] Wang W Z, Liu Y Z, Jiang P N. Numerical investigation on influence of real gas properties on nonlinear behavior of labyrinth seal-rotor system [J]. Applied Mathematics and Computation, 2015, 263: 12-24. [11] 钱新, 杜星文. 旋转Rayleigh梁动力学性能的研究[J]. 力学学报, 2011, 43(03): 635-640. QIAN Xin, DU Xingwen. Dynamic characteristics of spinning rayleigh beams [J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(03): 635-640. [12] 黄意新, 赵阳, 田浩, 等. 弹性支撑旋转Timoshenko梁动力学特性[J]. 噪声与振动控制, 2016, 36(03): 6-10+15. HUANG Yixin, ZHAO Yang, TIAN Hao, et al. Dynamic Characteristics of a Spinning Timoshenko Beam with Elastic Supports [J]. Noise and Vibration Control, 2016, 36(03): 6-10+15. [13] 黄意新, 穆洲, 郭明全, 等. 复杂边界条件轴向功能梯度梁动力学分析[J]. 哈尔滨工业大学学报, 2018, 50(10):143-150. HUANG Yixin, MU Zhou, GUO Mingquan, et al. Dynamic analysis of axially functionally graded beams with complexboundary conditions [J]. Journal of Harbin Institute of Technology, 2018, 50(10):143-150. [14] Mittendorf S C, Greif R. Vibrations of segmented beams by a fourier series component mode method [J]. Journal of Sound and Vibration, 1977, 55(3): 431-441. [15] Wang J T S, Lin C C. Dynamic analysis of generally supported beams using Fourier series [J]. Journal of Sound and Vibration, 1996, 196(3): 285-293. [16] Li W L. Free vibrations of beams with general boundary conditions [J]. Journal of Sound and Vibration, 2000, 237(4): 709-725. [17] Du J T, Li W L, Jin G Y, et al. An analytical method for the in-plane vibration analysis of rectangular plates with elastically restrained edges[J]. Journal of Sound and Vibration, 2007, 306(3): 908-927. [18] Li W L, Zhang X F, Du J T, et al. An exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports [J]. Journal of Sound and Vibration, 2008, 321(1): 254-269. [19] Xu D S, Du J T, Liu Z G. An accurate and efficient series solution for the longitudinal vibration of elastically restrained rods with arbitrarily variable cross sections [J]. Journal of Low Frequency Noise, Vibration and Active Control, 2019, 38(2): 403-414. [20] 许得水, 杜敬涛, 李文达, 等. 任意边界条件弹性杆结构扭转振动特性分析[J]. 振动与冲击, 2017, 36(01):161-166+174. XU Deshui, DU Jingtao, LI Wenda, et al. Torsional vibration characteristics of an elastic rod structure under arbitrary boundary conditions [J]. Journal of Vibration and Shock, 2017, 36(01): 161-166+174. [21] 鲍四元, 周静, 曹津瑞, 等. 端部任意弹性约束变截面地基梁的自由振动特性分析[J]. 应用力学学报, 2020, 37(05): 2228-2234+2335-2336. BAO Siyuan, ZHOU Jing, CAO Jinrui, et al. Free vibration analysis of foundation-beams with variable cross section and arbitrary elastic end-constraints [J]. Chinese Journal of Applied Mechanics, 2020, 37(05): 2228-2234+2335-2336. [22] 赵雨皓, 杜敬涛, 许得水. 轴向载荷条件下弹性边界约束梁结构振动特性分析[J]. 振动与冲击, 2020, 39(15): 109-117. ZHAO Yuhao, DU Jingtao, XU Deshui. Vibration characteristics analysis for an axially loaded beam with elastic boundary restraints [J]. Journal of Vibration and Shock, 2020, 39(15): 109-117. [23] 赵雨皓, 杜敬涛, 陈依林, 等. 具有非线性支撑和弹性边界约束的轴向载荷梁结构动力学行为研究[J]. 力学学报, 2022, 54(7): 2529-2542. ZHAO Yuhao, DU Jingtao, CHEN Yilin, et al. Dynamic behavior analysis of the axially loaded beam with the nonlinear support and elastic boundary constraints [J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 2529-2542 [24] 钟一谔, 何衍宗, 王正, 等. 转子动力学[M]. 北京: 清华大学出版社, 1987. [25] 袁惠群. 转子动力学基础[M]. 北京: 冶金工业出版社, 2013. [26] 杜敬涛. 任意边界条件下结构振动、封闭声场及其耦合系统建模方法研究[D]. 哈尔滨: 哈尔滨工程大学, 2009. [27] Banerjee J R, Su H. Development of a dynamic stiffness matrix for free vibration analysis of spinning beams[J]. Computers & Structures, 2004, 82(23-26): 2189-2197.