拱型结构在参、强激励下的非线性振动分析

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。

ANALYSIS OF NONLINEAR VIBRATION OF THE ARCH STRUCTURES UNDER THE PARAMETRIC AND FORCED EXCITING

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.