WANG Hao, CHEN Li-qun. Steady-State Amplitude-Frequency Characteristics of Axially Buckled Beams Under Strong Transverse Excitation[J]. Applied Mathematics and Mechanics, 2014, 35(2): 181-187. doi: 10.3879/j.issn.1000-0887.2014.02.006
 Citation: WANG Hao, CHEN Li-qun. Steady-State Amplitude-Frequency Characteristics of Axially Buckled Beams Under Strong Transverse Excitation[J]. Applied Mathematics and Mechanics, 2014, 35(2): 181-187.

# Steady-State Amplitude-Frequency Characteristics of Axially Buckled Beams Under Strong Transverse Excitation

##### doi: 10.3879/j.issn.1000-0887.2014.02.006
Funds:  The National Natural Science Foundation of China（11232009）
• Rev Recd Date: 2013-11-28
• Publish Date: 2014-02-15
• 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.
•  [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.

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142