中间约束轴向运动梁横向非线性振动
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摘要
聚焦于中间弹性约束对轴向运动梁横向非线性振动的影响。应用哈密顿原理,建立带有中间弹簧支撑的轴向运动梁的动力学控制方程。通过Galerkin截断方法数值计算了简支边界梯型截面轴向运动梁的固有频率,并数值计算得到梁的稳态响应。着重讨论了中间约束弹簧的刚度、系统的轴向运动速度、不同Galerkin截断阶数对系统固有频率、非线性受迫振动稳态响应的影响。研究发现,中间约束弹簧显著改变轴向运动梁的横向振动特性,而且轴向运动的速度能够改变中间弹簧对系统横向振动的影响。
Here, nonlinear vibration of an axially moving beam with an intermediate spring support was studied. With Hamilton's principle, its partial differential dynamic governing equation was established. Natural frequencies and steady-state responses of the beam with trapezoid cross-section and simply supported boundaries were numerically computed by means of Galerkin truncation method. The effects of intermediate spring stiffness, beam axially moving speed and Galerkin truncation orders on the system's natural frequencies and nonlinear forced vibration steady-state responses were discussed. The numerical results showed that intermediate spring significantly affects transverse vibration characteristics of the axially moving beam; the beam's axial motion speed can change effects of intermediate spring constraint on transverse vibration of the beam system.
Here, nonlinear vibration of an axially moving beam with an intermediate spring support was studied. With Hamilton's principle, its partial differential dynamic governing equation was established. Natural frequencies and steady-state responses of the beam with trapezoid cross-section and simply supported boundaries were numerically computed by means of Galerkin truncation method. The effects of intermediate spring stiffness, beam axially moving speed and Galerkin truncation orders on the system's natural frequencies and nonlinear forced vibration steady-state responses were discussed. The numerical results showed that intermediate spring significantly affects transverse vibration characteristics of the axially moving beam; the beam's axial motion speed can change effects of intermediate spring constraint on transverse vibration of the beam system.
引文
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[7] 杨鑫, 陈海波. 热冲击作用下轴向运动梁的振动特性研究[J]. 振动与冲击, 2017, 36(1): 8-15. YANG Xin, CHEN Haibo. Vibration characteristics of axially moving beam under thermal shock[J]. Journal of Vibration and Shock, 2017, 36(1): 8-15.
[8] 刘涛,罗梦翔,吴炜,等.有限元法的轴向运动梁的激励功率谱辨识[J]. 动力学与控制学报, 2016, 14(2): 186-192. LIU Tao, LUO Mengxiang, WU Wei, et al. Identification of excitation power spectrum density for an axially moving beam using finite element method[J]. Journal of Dynamics and Control, 2016, 14(2): 186-192.
[9] MARYNOWSKI K, KAPITANIAK T. Dynamics of axially moving continua[J]. International Journal of Mechanical Sciences, 2014, 81: 26-41.
[10] GROSSI R O, QUINTANA M V. The transition conditions in the dynamics of elastically restrained beams[J]. Journal of Sound and Vibration, 2008, 316: 274-297.
[11] GHAYESH M H, KAZEMIRAD S, DARABI M A. A general solution procedure for vibrations of systems with cubic nonlinearities and nonlinear/time-dependent internal boundary conditions[J]. Journal of Sound and Vibration, 330(22): 5382-5400.
[12] HOZHABROSSADATI S M, SANI A A, MOFID M. Free vibration analysis of a beam with an intermediate sliding connection joined by a mass-spring system[J]. Journal of Vibration and Control, 2016, 22: 955-964.
[13] BARRY O R, OGUAMANAM D C D, ZU J W. Nonlinear vibration of an axially loaded beam carrying multiple mass-spring-damper systems[J]. Nonlinear Dynamics, 2014, 77: 1597-1608.
[14] GHAYESH M H. Nonlinear transversal vibration and stability of an axially moving viscoelastic string supported by a partial viscoelastic guide[J]. Journal of Sound and Vibration, 2008, 314: 757-774.
[15] ZHANG Y W, ZHANG Z, CHEN L Q, et al. Impulse-induced vibration suppression of an axially moving beam with parallel nonlinear energy sinks[J]. Nonlinear Dynamics, 2015, 82: 61-71.
[2] 陈红永, 李上明. 轴向运动梁在轴向载荷作用下的动力学特性研究[J]. 振动与冲击, 2016, 35(19): 75-80. CHEN Hongyong, LI Shangming. The effect of axial load on dynamic characteristics of axially moving Timoshenko beam[J]. Journal of Vibration and Shock, 2016, 35(19): 75-80.
[3] 黄建亮, 陈树辉. 纵横向耦合轴向运动梁的自由振动响应研究[J]. 动力学与控制学报, 2010, 8(4): 316-321. HUANG Jianliang, CHEN Shuhui. Study on vibration of an axially moving bean with coupled transverse and longitudinal motions[J]. Journal of Dynamics and Control, 2010, 8(4): 316-321.
[4] 马国亮,徐明龙,陈立群,等. 末端质量作用下变长度轴向运动梁的振动特性[J]. 应用数学和力学, 2015, 36(9): 897-904. MA Guoliang, XU Minglong, CHEN Liqun, et al. Vibration characteristics of an axially moving variable length beam with a tip mass[J]. Applied Mathematics and Mechanics, 2015, 36(9): 897-904.
[5] 吕海炜, 李映辉, 刘启宽, 等. 轴向运动黏弹性夹层梁的横向振动[J]. 动力学与控制学报, 2013, 11(4): 314-319. Lü Haiwei, LI Yinghui, LIU Qikuan, et al. Transverse vibration of axially moving viscoelastic sandwich beam[J]. Journal of Dynamics and Control, 2013, 11(4): 314-319.
[6] 王杰, 胡宇达. 磁场中轴向运动载流梁磁弹性主共振分析[J]. 振动与冲击, 2016, 35(23): 65-73. WANG Jie, HU Yuda. Analysis of magneot-elastic principal resonance of axially moving current-carring beams in magnetic field[J]. Journal of Vibration and Shock, 2016, 35(23): 65-73.
[7] 杨鑫, 陈海波. 热冲击作用下轴向运动梁的振动特性研究[J]. 振动与冲击, 2017, 36(1): 8-15. YANG Xin, CHEN Haibo. Vibration characteristics of axially moving beam under thermal shock[J]. Journal of Vibration and Shock, 2017, 36(1): 8-15.
[8] 刘涛,罗梦翔,吴炜,等.有限元法的轴向运动梁的激励功率谱辨识[J]. 动力学与控制学报, 2016, 14(2): 186-192. LIU Tao, LUO Mengxiang, WU Wei, et al. Identification of excitation power spectrum density for an axially moving beam using finite element method[J]. Journal of Dynamics and Control, 2016, 14(2): 186-192.
[9] MARYNOWSKI K, KAPITANIAK T. Dynamics of axially moving continua[J]. International Journal of Mechanical Sciences, 2014, 81: 26-41.
[10] GROSSI R O, QUINTANA M V. The transition conditions in the dynamics of elastically restrained beams[J]. Journal of Sound and Vibration, 2008, 316: 274-297.
[11] GHAYESH M H, KAZEMIRAD S, DARABI M A. A general solution procedure for vibrations of systems with cubic nonlinearities and nonlinear/time-dependent internal boundary conditions[J]. Journal of Sound and Vibration, 330(22): 5382-5400.
[12] HOZHABROSSADATI S M, SANI A A, MOFID M. Free vibration analysis of a beam with an intermediate sliding connection joined by a mass-spring system[J]. Journal of Vibration and Control, 2016, 22: 955-964.
[13] BARRY O R, OGUAMANAM D C D, ZU J W. Nonlinear vibration of an axially loaded beam carrying multiple mass-spring-damper systems[J]. Nonlinear Dynamics, 2014, 77: 1597-1608.
[14] GHAYESH M H. Nonlinear transversal vibration and stability of an axially moving viscoelastic string supported by a partial viscoelastic guide[J]. Journal of Sound and Vibration, 2008, 314: 757-774.
[15] ZHANG Y W, ZHANG Z, CHEN L Q, et al. Impulse-induced vibration suppression of an axially moving beam with parallel nonlinear energy sinks[J]. Nonlinear Dynamics, 2015, 82: 61-71.