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拱型结构在参、强激励下的非线性振动分析
引用本文:刘习军,陈予恕,侯书军.拱型结构在参、强激励下的非线性振动分析[J].力学学报,2000,32(1):99-104.
作者姓名:刘习军  陈予恕  侯书军
作者单位:天津大学机械学院,天津,300072
基金项目:国家自然科学基金!19990510
摘    要:利用数值解析法研究了拱型结构在参数激励与强迫激励联合作用下的非线性振动特性。得到了轴向力与固有频率的关系及轴向力对发生主共振,1/2亚谱共振的影响,由于1/2亚谐共振是高频激振低频响应,是最危险区域,应得到足够的重视,为工程设计提供了可靠的理论依据。

关 键 词:拱型结构  参数激励  非线性振动

ANALYSIS OF NONLINEAR VIBRATION OF THE ARCH STRUCTURES UNDER THE PARAMETRIC AND FORCED EXCITING
Liu Xijun,Chen Yushu,Hou Shujun.ANALYSIS OF NONLINEAR VIBRATION OF THE ARCH STRUCTURES UNDER THE PARAMETRIC AND FORCED EXCITING[J].chinese journal of theoretical and applied mechanics,2000,32(1):99-104.
Authors:Liu Xijun  Chen Yushu  Hou Shujun
Abstract:Arch structures are widely used in support structure of aircraft or mechanical arm ofrobot, because of extreme light weight and extremely flexible and heavy load be used at the sametime in the systems make them exhibit abundant dynamical phenomena, it has attracted extensive attentioon of researchers. The complicated shape of the arch structures adds difficulties to thedynamical analyzing of such systems, therefore, a numerical-analytical method (it is combining afinite element method with a approximate analytical method) was put forward in this paper toovercome this difficulties, a nonlinear vibration equation of arch structures under the parametricand forced exciting was establish by means of numerical-analytical method also. The first orderapproximate analytical solution in the cases of the primary resonance () and the 1/2 subharmonic resonance (/2) was derived by means of the averaging method. It was shown thatin the case of primajry resonance, the forced exciting plays a domainant role, but in the case of 1/2subharmonic resonance, the parametrical exciting. The effects of the axial force on the primaryresonance and the sub-harmonic resonance as well as the relation between the axial force. andnatural frequency were obtained. The amplitude-frequency curve given out by the approlximateanalytical and the numerical results in both the primary resonance and the sub-harmonic resonancecases, and in the case of 1/2 subharmonic resonance, the response history during starting stage wasprovided also. It should be pointed out that the 1/2 subharmonic resonance is the low. frequencyresponse caused when the high frequency exciting, which may results in serious consequencgs; soit obtain enough attention. The conclusions of this paper provide a scientific theory basis for theengineering design of the arch structures. And the numerical-analytical method put forward inthis paper provides a new and reliable method for the analysis of nonlinear vibration in one planeof the complicated shaped arch elements.
Keywords:arch structures  nonlinear vibration  parametric and forced excitation  1/2 subharmonic resonance
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