Steady-State Amplitude-Frequency Characteristics of Axially Buckled Beams Under Strong Transverse Excitation
-
摘要: 研究均匀各向同性黏弹性屈曲梁受基座简谐运动激励的横向非线性振动.在简支边界条件和强外激励的作用下,基于二阶Galerkin方法截断导出的数学模型,用多尺度法分析了存在1∶2内共振时的主共振,由可解性条件导出稳态响应.发现幅频响应曲线存在多种跳跃现象.考察了各系数尤其是轴向压力对幅频响应曲线的影响Abstract: A nonlinear vibration analysis was conducted to determine the steady-state response of simply-supported viscoelastic axially buckled beams to harmonic base excitation. Based on the 2-order Galerkin truncation of the governing equation, and in the case of strong excitation, the solvability condition was derived with the multiple-scale method in the presence of 1∶2 internal resonance, to analyze the primary strong external resonance. Various jumping phenomena were revealed in the amplitude-frequency characteristic curves, and the effects of related parameters, especially the axial force, on the phenomena were examined.
-
Key words:
- nonlinearity /
- viscoelasticity /
- buckled beam /
- forced vibration /
- amplitude-frequency characteristics
-
[1] 周哲玮. 屈曲杆大挠度弹性曲线的摄动解及其不完全分岔问题的奇异摄动解法[J]. 应用数学和力学, 1987,8(4): 337-345.(ZHOU Zhe-wei. The perturbation solution of the large elastic curve of buckled bars and the singular perturbation method for its imperfect bifurcation problem[J]. Applied Mathematics and Mechanics,1987,8(4): 337-345.(in Chinese)) [2] 李庆明. 弹性杆的动态屈曲模态[J]. 应用数学和力学, 1990,11(1): 61-66.(LI Qing-ming. Dynamic buckling mode of an elastic bar[J]. Applied Mathematics and Mechanics,1987,11(1): 61-66.(in Chinese)) [3] Abou-Rayan A M, Nayfeh A H, Mook D T, Nayfeh M A. Nonlinear response of a parametrically excited buckled beam[J]. Nonlinear Dynamics, 1993, 4(5): 499-525. [4] 张年梅, 杨桂通. 非线性弹性梁在谐波激励下的次谐和超次谐响应[J]. 应用数学和力学, 1999,20(12): 1224-1228.(ZHANG Nian-mei, YANG Gui-tong. Subharmonic and ultra-subharmonic response of nonlinear elastic beams subjected to harmonic excitation[J]. Applied Mathematics and Mechanics,1999,20(12): 1224-1228.(in Chinese)) [5] Eman S A, Nayfeh A H. On the nonlinear dynamics of a buckled beam subject to a primary-resonance excitation[J]. Nonlinear Dynamics, 2004, 35(1): 1-17. [6] 朱媛媛, 胡育佳, 程昌钧. Euler型梁-柱结构的非线性稳定性和后屈曲分析[J]. 应用数学和力学, 2011,32(6): 674-682.(ZHU Yuan-yuan, HU Yu-jia, CHENG Chang-jun. Analysis of non-linear stability and post-buckling for the Euler-type beam-column structure[J]. Applied Mathematics and Mechanics,2011,32(6): 674-682.(in Chinese)) [7] Lestari W, Hanagud S. Nonlinear vibration of buckled beam: some exact solutions[J].International Journal of Solids and Structures, 2001, 38(26/27): 4741-4757. [8] 王昊, 张艳雷, 陈立群. 轴向受力屈曲梁受迫振动的稳态响应[J]. 上海大学学报. doi: 103969/j.issn.1007-2861.2013.07.025.(WANG Hao, ZHANG Yan-lei, CHEN Li-qun. The steady-state response of forced vibration for a buckling beam under axial press[J]. Journal of Shanghai University . doi: 103969/j.issn.1007-2861.2013.07.025.) [9] 刘延柱, 陈立群. 非线性振动[M]. 北京: 高等教育出版社, 2001.(LIU Yan-zhu, CHEN Li-qun. Nonlinear Vibration [M]. Beijing: Higher Education Press, 2001.(in Chinese)) [10] Nayfeh A H, Mook D T. Nonlinear Oscillations [M]. New York: Wiley-Interscience, 1979.
点击查看大图
计量
- 文章访问数: 992
- HTML全文浏览量: 76
- PDF下载量: 1097
- 被引次数: 0