The Incremental Harmonic Balance (IHB) method was used to analyze nonlinear dynamics of rectangular thin plate with four simply supported sides, subjected to the external two-tone transverse harmonic excitation. Based on the vibration differential equation of thin plate, the non-dimensional Duffing nonlinear forced vibration equation was deduced by using Galerkin method. Introducing multiple time variables defined as , in which were the nonlinear frequencies of responses incommensurable with one another, corresponding calculation process of IHB method was derived. As a numerical example, time histories diagrams, spectrum diagrams, phase diagrams and Poincaré section were presented by IHB method with different excitations, and quasi-periodic motions of the plate which undergo the external multi-excitations were obtained. Meanwhile the results obtained from the IHB method are in good agreement with the results obtained from the numerical integration method.
Key words
rectangular thin plate /
nonlinear vibration /
Incremental Harmonic Balance method /
multiple force excitations /
quasi-periodic motion
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
References
[1] M. Amabili,S.Carra. Thermal effects on geometrically nonlinear vibrations of rectangular plates with fixed edges[J]. Journal of Sound and Vibration, 2009, 321: 936-954.
[2] Marynowski K. Free vibration analysis of the axially moving levy-type viscoelastic plate[J]. European Journal of Mechanics-A/Solids, 2010, 29(5): 879-886.
[3] V. Dogan. Nonlinear vibration of FGM plates under random excitation [J]. Composite Structures, 2013, (95): 366-374.
[4] 张亚辉, 马永彬. 薄板振动分析的辛空间波传播方法. 振动与冲击, 2014, 33(12): 1-7.
ZHANG Ya-hui, MA Yong-bin. A wave propagation method in symplectic space for vibration analysis of thin plates[J]. Journal of Vibration and Shock, 2014, 33(12): 1-7.
[5] 杨坤, 梅志远, 李华东. 粘弹性复合材料夹芯板稳态响应分析. 振动与冲击, 2013, 32(7): 88-92.
YANG Kun, MEI Zhi-yuan, LI Hua-dong. Steady response analysis for a composite sandwich plate with viscoelastic core layer based on Kelvin model[J]. Journal of Vibration and Shock, 2013, 32 (7): 88-92.
[6] 吕书锋, 胡宇达. 正交各向异性叠层板的非线性主共振分析. 动力学与控制学报, 2009, 7(1): 35-38.
Shu-feng, HU Yu-da. Nonlinear principal resonance of orthotropic laminated plates[J]. Journal of Dynamics and Control, 2009, 7 (1): 35-38.
[7] 徐芝纶. 弹性力学. 北京: 高等教育出版社, 2006.
XU Zhi-lun. Elastic mechanics[M]. Beijing: Higher Education Press, 2006.
[8] 陈树辉, 黄建亮, 佘锦炎. 轴向运动梁横向非线性振动研究. 动力学与控制学报, 2004, 2(1): 40-45.
CHEN Shu-hui, HUANG Jian-liang, SHE Jin-yan. Study on the laterally nonlinear vibration of axially moving beams[J]. Journal of Dynamics and Control, 2004, 2(1): 40-45.
[9] Chia C Y. Nonlinear analysis of plates[M]. New York: McGraw-Hill,1980.
[10] 黄安基. 非线性振动. 成都: 西南交通大学 出版社, 1993.
HUANG An-ji. Nonlinear vibration[M].
Chengdu: Southwest Jiaotong University Press, 1993.
[11] 陈树辉. 强非线性振动系统的定量分析方法. 北京: 科学出版社, 2007.
CHEN Shu-hui. Method for quantitative analysis of strongly nonlinear vibration system[M]. Beijing: Science Press, 2007.
[12] Pušenjak, R.R., Oblak, M.M., Incremental harmonic dynamical systems with cubic non-linearities. International Journal for Numerical Methods in Engineering, 2004, 59: 255-269.
{{custom_fnGroup.title_en}}
Footnotes
{{custom_fn.content}}