索-梁耦合结构非线性分析

PDF(1641 KB)

振动与冲击 ›› 2015, Vol. 34 ›› Issue (14) : 147-152.

论文

索-梁耦合结构非线性分析

刘海涛1，魏明海2，肖仪清1，林坤1

作者信息 +

Nonlinear response analysis of a cable-beam coupled system

LIU Hai-tao1，WEI Ming-hai 2，XIAO Yi-qing1，LIN Kun1

Author information +

文章历史 +

摘要

研究内、外共振联合激励下索-梁耦合结构的非线性行为，用多尺度法探讨索-梁耦合结构内共振模式。分析表明，耦合结构存在多种内共振形式；考虑梁与索在1:2内共振作用下分别研究索-梁耦合结构在梁主共振且索自参数共振时与梁亚谐波共振且索主参数共振时的非线性特性，并具体讨论索-梁耦合结构的垂跨比、质量比、刚度比及外激励幅值等参数对索-梁耦合结构中梁、索的非线性特性影响。研究表明，由于模态耦合影响，索-梁耦合结构存在两种外共振机制，梁表现出非线性特性，索表现出两自由度特性；刚度比参数对耦合结构非线性特性有显著影响。

Abstract

Combined with quantitative analysis of the nonlinear vibration method, the nonlinear response of cable and beam as a coupled structure under the combined effects of internal and external resonance is investigated. Applied the method of multiple scales to the cable-beam coupled structure, analyzing the possible resonances between the mode of the beam and cable, and pointing out its forms. Considering the resonance 1:2 between the beam and cable, the nonlinear response of the cable-beam coupled structure under the primary resonance of the beam (auto-parametric resonance of the cable) and the principal parametric resonance of cable (sub-harmonic resonance of the beam) are respectively investigated. The effects of the cable sag to span ratio, mass ratio and stiffness ratio on the nonlinear responses are investigated follow. Last, in order to validate the correctness of the approximate solution, the displacement of the first order approximate analytical solution of the beam and cable are contrast to the numerical solution. The results show good agreement between the analytical and numerical solutions especially near the external resonance frequency.

导出引用

刘海涛1，魏明海2，肖仪清1，林坤1. 索-梁耦合结构非线性分析[J]. 振动与冲击, 2015, 34(14): 147-152

LIU Hai-tao1，WEI Ming-hai 2，XIAO Yi-qing1，LIN Kun1. Nonlinear response analysis of a cable-beam coupled system[J]. Journal of Vibration and Shock, 2015, 34(14): 147-152

参考文献

[1] Nayfeh A H, Arafat H N, Chin C M,et al. Multi-mode interactions in suspended cables[J]. Journal of Sound and Vibration,2002,8: 337-387.
[2] 王波, 徐丰, 张海龙. 端部激励下空间倾斜拉索非线性振动特性研究[J]. 振动与冲击,2009,28(5):172-175.
WANG Bo, XU Feng, ZHANG Hai-long. Non-linear vibration characteristics of spatial inclined cables under periodic support excitation[J]. Journal of Vibration and Shock, 2009,28(5):172- 175.
[3] 吴晓, 黎大志, 罗佑新. 斜拉索非线性固有振动特性分析[J]. 振动与冲击, 2003,22(3):34-39.
WU Xiao, LI Da-zhi, LUO You-xin. Nonlinear natural vibration character analysis of stay cables[J]. Journal of Vibration and Shock, 2003,22(3):34-39.
[4] Ghayesh M H. Subharmonic dynamics of an axially accelerating beam[J]. Archive of Applied Mechanics, 2012, 82: 1169-1181.
[5] 罗帅, 刘红军, 王刚. 考虑桥面运动的斜拉索减振模型[J]. 深圳大学学报(理工版),2010,27(4):471-473.
LUO Shuai, LIU Hong-jun, WANG Gang. The characteristic of stay-cable damping system in consideration of bridge deck vibration[J].Journal of Shenzhen University Science and Engineering, 2010,27(4):471-473.
[6] Fujino Y, Warnitchai P, Pacheco B M. An experimental and analytical study of autoparametric resonance in a 3DOF model of cable-stayed-beam[J]. Nonlinear Dynamics, 1993,4:111-138.
[7] Xia Y, Fujino Y.Auto-parametric vibration of a cable-stayed-
beam structure under random excitation[J]. Journal of Engineering Mechanics-Asce, 2006,132:279-286.
[8] Fung R F, Lu LY, Huang S C. Dynamic modelling and vibration analysis of a flexible cable-stayed beam structure[J]. Journal of Sound and Vibration, 2002, 254(4): 717-726.
[9] Gattulli V, Morandini M, Paolone A. A parametric analytical model for non-linear dynamics in cable-stayed beam[J]. Earthquake Engineering & Structural Dynamics, 2002,31: 1281-
1300.
[10] Gattulli V, Lepidi M. Nonlinear interactions in the planar dynamics of cable-stayed beam[J]. International Journal of Solids and Structures, 2003,40:4729-4748.
[11] Gattulli V, Lepidi M, Mjh G, et al. One-to-two global-local interaction in a cable-stayed beam observed through analytical, finite element and experimental models[J]. International Journal of Non-Linear Mechanics, 2005,40:571-588.
[12] 王涛，沈锐利，李洪.斜拉桥索-梁相关振动概念及其研究方法初探[J].振动与冲击,2013,32(20):29-34.
WANG Tao, SHEN Rui-li, LI Hong. Primary exploration for concept and studying method of cable-beam vibration in a cable-stayed bridge[J].Journal of Vibration and Shock,2013,
32(20):29-34.
[13] 赵跃宇, 蒋丽忠, 王连华,等. 索-梁组合结构的动力学建模理论及其内共振分析[J]. 土木工程学报, 2004,37:69-72.
ZHAO Yue-yu, JIANG Li-zhong, WANG Lian-hua,et al. The dynamical modeling theory and internal resonance of cable-
beam composite structure[J]. China Civil Engineering Journal, 2004,37:69-72.
[14] 赵跃宇, 杨相展, 刘伟长,等. 索-梁组合结构中拉索的非线性响应[J]. 工程力学, 2006,23(11):153-158.
ZHAO Yue-yu, YANG Xiang-zhan, LIU Wei-chang,et al. Nonlinear response of cables in cable-stayed beam structure[J]. Engineering Mechanics, 2006,23(11):153-158.
[15] 冯维明, 高黎黎, 金栋平. 索-梁耦合系统解的稳定性分析[J]. 应用力学学报, 2008,25(2):284-288.
FENG Wei-ming, GAO Li-li, JIN Dong-ping. Nonlinear dynamic analysis for coupled structure of cable-stayed beam[J]. Chinese Journal of Applied Mechanics, 2008,25(2):284-288.
[16] 冯维明, 高黎黎. 索-梁耦合系统非线性振动分析[J]. 振动工程学报, 2008,21(2):115-119.
FENG Wei-ming, GAO Li-li. Nonlinear vibration analysis for coupled structure of cable-stayed beam[J]. Journal of Vibration Engineering, 2008,21(2):115-119.
[17] Wei M H, Xiao Y Q, Liu H T. Bifurcation and chaos of a cable–beam coupled system under simultaneous internal and external resonances[J]. Nonlinear Dynamics, 2012, 67(3):1969- 1984.