Winkler地基上材料非线性矩形薄板的主共振

杨志安; 韩彦斌

Winkler地基上材料非线性矩形薄板的主共振

杨志安¹,
韩彦斌²

详细信息

作者简介:
杨志安(1963- ),男,教授,博士,研究方向为机电耦联非线性动力学及结构与振动工程,电话:0315-2028305,E-mail:yangzhian@eyou.com

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出版历程
- 收稿日期: 2006-01-09
- 刊出日期: 2007-02-25

Primary Resonance of Thin Rectangular Plate with Material Nonlinearity on Winkler Foundation

YANG Zhian¹,
HAN Yanbin²

摘要

摘要: 为了研究Winkler地基上材料非线性矩形薄板受简谐激励的非线性振动,应用弹性力学理论,建立了其动力学方程,并用Galerkin方法将其转化为非线性振动方程.应用非线性振动的多尺度法,求得系统主共振的近似解,并进行了数值计算.研究表明,随着阻尼系数、几何参数和激励幅值的改变,主共振响应曲线有跳跃和滞后现象,振幅随阻尼系数的增大而减小.此外,还对系统主共振响应方程进行了奇异性分析,得到了开折参数平面的转迁集和分岔图.
- 主共振 /
- 非线性 /
- Winkler地基 /
- Galerkin方法 /
- 多尺度法 /
- 奇异性
Abstract: Based on the elastic theory,nonlinear dynamical equations for an externally excited thin rectangular plate on the Winkler foundation were established by considering meterial nonlinearity in order to investigate its nonlinear vibration,and the corresponding nonlinear vibration equation was obtained using the Galerkin’s method.By means of the method of multiple scales for nonlinear oscillations,the approximate solution of primary resonance of the system was acquired,and a numerical analysis was carried out.The research shows that jump and hysteresis phenomena exist in the amplitude-frequency response curves with the changing of damping factor,geometric parameters and excitation,the amplitude decreases with the increase of damping.In addition,the amplitude-frequency response equation was investigated,and the transition variety and bifurcation diagram of unfolding parameter plane were obtained based on the singularity theory.
- primary resonance /
- nonlinearity /
- Winkler foundation /
- the Galerkin’s method /
- method of multiple scales /
- singularity

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参考文献(1)

曲庆章,梁兴复.弹性地基上自由矩形板的非线性动静态分析[J].工程力学,1996,13(3):40-46.QU Qingzhang,LIANG Xingfu.Nonlinear analysis of free rectangular plate on elastic foundation[J].Engineering Mechanics,1996,13(3):40-46.[2] GAJIENDAR N.Large amplitude vibrations of plates on elastic foundation[J].International Journal of Nonlinear Mechanics,1967,2(1):163-168.[3] NATH Y.Large amplitude response of circular plate on elastic foundation[J].International Journal of Nonlinear Mechanics,1982,17(4):285-296.[4] DUMIR P C.Nonlinear vibration and postbucking of isotropic thin circular plate on elastic foundation[J].Journal of Sound and Vibration,1986,107(2):253-263.[5] 邱平,王新志.非线性弹性地基上的圆薄板的分岔与混沌问题[J].应用数学和力学,2003,24(8):779-784.QIU Ping,WANG Xinzhi.Bifurcation and chaos problem of thin circular plate on nonlinear elastic foundation[J].Applied Mathematics and Mechanics,2003,24(8):779-784.[6] 杨志安,李文兰.弹性地基上四边自由矩形大挠度薄板复杂运动研究[J].唐山学院学报,2005,18(1):81-84.YANG Zhian,LI Wenlan.Reasearch on complex vibration of large deflection of thin rectangular plate with four free edges on elastic foundation[J].Journal of Tangshan College,2005,18(1):81-84.[7] 杨志安,赵雪娟,席晓燕.非线性弹性地基上矩形薄板的主参数共振[J].岩土力学,2005,26(12):1 921-1 925.YANG Zhian,ZHAO Xuejuan,Xl Xiaoyan.Primary parametric resonance of thin rectangular plate on nonlinear elastic foundation[J].Rock and Soil Mechanics,2005,26(12):1 921-1 925.[8] 韩强.非线性弹性矩形板的自由振动[J].华南理工大学学报,2000,28(7):78-82.HAN Qiang.Nonlinear vibration of a rectangular plate with physical nonlinear[J].Journal of South China University of Technology,2000,28(7):78-82.[9] NAYFEH A H,MOOK D T.Nonlinear oscillations[M].New York:Wiley-Interscience,1979:99-137.[10] GOLUBISKY M,SCHAEFFER D G.Singularities and groups in bifurcation theory[M].New York:Springer-Verlag,1985:266-297.

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文章访问数: 1440
HTML全文浏览量: 64
PDF下载量: 304
被引次数: 0

Winkler地基上材料非线性矩形薄板的主共振

作者简介: 杨志安(1963- ),男,教授,博士,研究方向为机电耦联非线性动力学及结构与振动工程,电话:0315-2028305,E-mail:yangzhian@eyou.com

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出版历程

Primary Resonance of Thin Rectangular Plate with Material Nonlinearity on Winkler Foundation

计量

出版历程

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作者简介:
杨志安(1963- ),男,教授,博士,研究方向为机电耦联非线性动力学及结构与振动工程,电话:0315-2028305,E-mail:yangzhian@eyou.com