Vibration of axially moving beam supported by viscoelastic foundation

doi:10.1007/s10483-017-2170-9

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (2): 161-172.doi: https://doi.org/10.1007/s10483-017-2170-9

Vibration of axially moving beam supported by viscoelastic foundation

Haijuan ZHANG^1,2, Jian MA², Hu DING^1,3, Liqun CHEN^1,3,4

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
2. School of Mechanical Engineering, Anhui University of Technology, Maanshan 243032, Anhui Province, China;
3. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;
4. Department of Mechanics, College of Sciences, Shanghai University, Shanghai 200444, China

收稿日期:2016-05-16 修回日期:2016-09-25 出版日期:2017-02-01 发布日期:2017-02-01
通讯作者: Liqun CHEN,E-mail:lqchen@staff.shu.edu.cn E-mail:lqchen@staff.shu.edu.cn
基金资助:
Project supported by the State Key Program of the National Natural Science Foundation of China (No.11232009) and the National Natural Science Foundation of China (Nos.11372171 and 11422214)

Vibration of axially moving beam supported by viscoelastic foundation

Haijuan ZHANG^1,2, Jian MA², Hu DING^1,3, Liqun CHEN^1,3,4

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
2. School of Mechanical Engineering, Anhui University of Technology, Maanshan 243032, Anhui Province, China;
3. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;
4. Department of Mechanics, College of Sciences, Shanghai University, Shanghai 200444, China

Received:2016-05-16 Revised:2016-09-25 Online:2017-02-01 Published:2017-02-01
Contact: Liqun CHEN E-mail:lqchen@staff.shu.edu.cn
Supported by:
Project supported by the State Key Program of the National Natural Science Foundation of China (No.11232009) and the National Natural Science Foundation of China (Nos.11372171 and 11422214)

摘要/Abstract

摘要：

In this paper, transverse vibration of an axially moving beam supported by a viscoelastic foundation is analyzed by a complex modal analysis method. The equation of motion is developed based on the generalized Hamilton's principle. Eigenvalues and eigenfunctions are semi-analytically obtained. The governing equation is represented in a canonical state space form, which is defined by two matrix differential operators. The orthogonality of the eigenfunctions and the adjoint eigenfunctions is used to decouple the system in the state space. The responses of the system to arbitrary external excitation and initial conditions are expressed in the modal expansion. Numerical examples are presented to illustrate the proposed approach. The effects of the foundation parameters on free and forced vibration are examined.

关键词: natural frequency, viscoelastic foundation, forced vibration, axially moving beam, complex modal analysis

Abstract:

Key words: natural frequency, forced vibration, axially moving beam, viscoelastic foundation, complex modal analysis

中图分类号:

O326

Haijuan ZHANG, Jian MA, Hu DING, Liqun CHEN. Vibration of axially moving beam supported by viscoelastic foundation[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(2): 161-172.

参考文献

[1] Bhat, R. B., Xistris, G. D., and Sanker, T. S. Dynamic behavior of a moving belt supported on elastic foundation. Journal of Mechanics Design, 104, 143-147(1982)
[2] Perkins, N. C. Linear dynamics of a translating string on an elastic foundation. Journal of Vibration and Acoustics, 112, 2-7(1990)
[3] Wickert, J. A. Response solutions for the vibration of a traveling string on an elastic foundation. Journal of Vibration and Acoustics, 116, 137-139(1994)
[4] Xiong, Y. and Hutton, S. G. Vibration and stability analysis of a multi-guided rotating string. Journal of Sound and Vibration, 169, 669-683(1994)
[5] Tan, C. A. and Zhang, L. Dynamic characteristics of a constrained string translating across an elastic foundation. Journal of Vibration and Acoustics, 116, 318-325(1994)
[6] Riedel, C. H. and Tan, C. A. Dynamic characteristics and mode localization of elastically constrained axially moving strings and beams. Journal of Sound and Vibration, 215, 455-473(1998)
[7] Saeed, H. M. and Festroni, F. Simulation of combined system by periodic structures:the wave transfer matrix approach. Journal of Sound and Vibration, 213, 53-73(1998)
[8] Parker, R. G. Supercritical speed stability of the trivial equilibrium of an axially-moving string on an elastic foundation. Journal of Sound and Vibration, 221, 205-219(1999)
[9] Jha, R. K. and Parker, R. G. Spatial discretization of axially moving media vibration problems. Journal of Vibration and Acoustics, 122, 290-294(2000)
[10] Kartik, V. and Wickert, J. A. Vibration and guiding of moving media with edge weave imperfections. Journal of Sound and Vibration, 291, 419-436(2006)
[11] Yurdda?. A., Özkaya, E., and Boyac?, H. Nonlinear vibrations of axially moving multi-supported strings having non-ideal support condition. Nonlinear Dynamics, 73, 1223-1244(2012)
[12] Yang, X. D., Lim, C. W., and Liew, K. M. Vibration and stability of an axially moving beam on elastic foundation. Advances in Structural Engineering, 13, 241-248(2010)
[13] Ba?atli, S. M., Özkaya, E., and Öz, H. R. Dynamics of axially accelerating beams with an inte rmediate support. Journal of Vibration and Acoustics, 133, 470-476(2011)
[14] Ba?atli, S. M., Özkaya, E., and Öz, H. R. Dynamics of axially accelerating beams with multip le supports. Nonlinear Dynamics, 74, 237-255(2013)
[15] Kural, S. and Özkaya, E. Vibrations of an axially accelerating, multiple supported flexible beam. Structural Engineering and Mechanics, 44, 521-538(2012)
[16] Ghayesh, M. H. Stability and bifurcations of an axially moving beam with an intermediate spring support. Nonlinear Dynamics, 69, 193-210(2012)
[17] Yang, Y., Ding, H., and Chen, L. Q. Dynamic response to a moving load of a Timoshenko beam resting on a nonlinear viscoelastic foundation. Acta Mechanica Sinica, 29, 718-727(2013)
[18] Sun, L. A closed-form solution of a Bernoulli-Euler beam on a viscoelastic foundation under harmonic line loads. Journal of Sound and Vibration, 242, 619-627(2001)
[19] Ghayesh, M. H. Nonlinear transversal vibration and stability of an axially moving viscoelastic string supported by a partial viscoelastic guide. Journal of Sound and Vibration, 314, 757-774(2008)
[20] Ahmadian, M. T., Nasrabadi, V. Y., and Mohammadi, H. Nonlinear transversal vibration of an axially moving viscoelastic string on a viscoelastic guide subjected to mono-frequency excitation. Acta Mechanica, 214, 357-373(2010)
[21] Li, X. J. and Chen, L. Q. Modal analysis of coupled vibration of belt drive systems. Applied Mathematics and Mechanics(English Edition),29(1), 9-13(2008) DOI 10.1007/s10483-008-0102-x
[22] Huang, L. H. and Liu, X. T. Eigenvalue and stability analysis for transverse vibrations of axially moving strings based on Hamiltonian dynamics. Acta Mechanica Sinica, 21, 485-494(2005)
[23] Chung, C. H. and Kao, I. Modeling of axially moving wire with damping:eigenfunctions, orthogonality and applications in slurry wiresaws. Journal of Sound and Vibration, 330, 2947-2963(2011)
[24] Ding, H. and Jean, W. Z. Steady-state responses of pulley-belt systems with a one-way clutch and belt bending stiffness. Journal of Vibration and Acoustics, 136, 041006(2014)
[25] Ding, H., Zhang, G. C., Chen, L. Q., and Yang, S. P. Forced vibrations of supercritically transporting viscoelastic beams. Journal of Vibration and Acoustics, 134, 051007(2012)
[26] Zhang, H. J. and Chen, L. Q. Vibration of an axially moving string supported by a viscoelastic foundation. Acta Mechanica Solida Sinica, 26(3), 221-231(2016)
[27] Yan, Q. Y., Ding, H., and Chen, L. Q. Nonlinear dynamics of an axially moving viscoelastic Timoshenko beam under parametric and external excitations. Applied Mathematics and Mechanics (English Edition), 36(8), 971-984(2015) DOI 10.1007/s10483-015-1966-7
[28] Ding, H. Steady-state responses of a belt-drive dynamical system under dual excitations. Acta Mechanics Sinica, 32, 156-169(2016)

Vibration of axially moving beam supported by viscoelastic foundation

Vibration of axially moving beam supported by viscoelastic foundation

PDF

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	A. RAHMANI, S. FAROUGHI, M. SARI. On wave dispersion of rotating viscoelastic nanobeam based on general nonlocal elasticity in thermal environment[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(9): 1577-1596.
[2]	Bo DOU, Hu DING, Xiaoye MAO, Sha WEI, Liqun CHEN. Dynamic modeling of fluid-conveying pipes restrained by a retaining clip[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(8): 1225-1240.
[3]	Wenhao YUAN, Haitao LIAO, Ruxin GAO, Fenglian LI. Vibration and sound transmission loss characteristics of porous foam functionally graded sandwich panels in thermal environment[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(6): 897-916.
[4]	Ying MENG, Xiaoye MAO, Hu DING, Liqun CHEN. Nonlinear vibrations of a composite circular plate with a rigid body[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(6): 857-876.
[5]	U. N. ARIBAS, M. AYDIN, M. ATALAY, M. H. OMURTAG. Cross-sectional warping and precision of the first-order shear deformation theory for vibrations of transversely functionally graded curved beams[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(12): 2109-2138.
[6]	Jingming FAN, Bo CHEN, Yinghui LI. Closed-form steady-state solutions for forced vibration of second-order axially moving systems[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(10): 1701-1720.
[7]	Zhaonian LI, Juan LIU, Biao HU, Yuxing WANG, Huoming SHEN. Wave propagation analysis of porous functionally graded piezoelectric nanoplates with a visco-Pasternak foundation[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(1): 35-52.
[8]	Guanzhong LIU, Xingming GUO, Li ZHU. Dynamic analysis of wind turbine tower structures in complex ocean environment[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(7): 999-1010.
[9]	Hu DING, Minhui ZHU, Liqun CHEN. Dynamic stiffness method for free vibration of an axially moving beam with generalized boundary conditions[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(7): 911-924.
[10]	Dongxing CAO, Yanhui GAO. Free vibration of non-uniform axially functionally graded beams using the asymptotic development method[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(1): 85-96.
[11]	H. S. ZHAO, Y. ZHANG, S. T. LIE. Frequency equations of nonlocal elastic micro/nanobeams with the consideration of the surface effects[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(8): 1089-1102.
[12]	Xiaodong YANG, Shaowen WANG, Wei ZHANG, Zhaohong QIN, Tianzhi YANG. Dynamic analysis of a rotating tapered cantilever Timoshenko beam based on the power series method[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(10): 1425-1438.
[13]	Qianli ZHAO, Zhili SUN. In-plane forced vibration of curved pipe conveying fluid by Green function method[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(10): 1397-1414.
[14]	M. HAJHOSSEINI, M. RAFEEYAN. Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(8): 1053-1066.
[15]	Xuan WANG, Shirong LI. Free vibration analysis of functionally graded material beams based on Levinson beam theory[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(7): 861-878.