圆弧拱的面内非线性动力学分析

对圆弧拱面内自由振动的频率和非线性内共振现象进行了研究.通过假设满足位移边界条件的振型函数对圆弧拱的面内非线性方程进行Galerkin一阶模态截断,先对派生系统的线性频率进行求解,就不同参数对频率的影响进行分析;然后利用多尺度法对离散模型进行求解.结果表明:截面高度对径向振动频率有显著影响,但是对切向振动频率影响很小;另外,就本文方程而言,可能存在三种内共振形式,但内共振现象的产生与否还决定于圆弧拱的边界条件.

In plane nonlinear dynamic analysis of circular arches

The in-plane free vibration frequencies and nonlinear internal resonance of circular arches were studied. Based on the assumptive vibration function, the nonlinear equations were discretized by the Galerkin method. First, the frequencies of derived system were obtained, thus the effect of different parameters on frequencies were studied. Then, the method of multiple scales was applied to solve the equations. The results showed that the radial frequency was greatly affected by the height of the cross-section, but the tangential frequency wasn't. Three types of internal resonance form may be activated. The further studies of the equations in this paper pointed out that internal resonance was determined by the boundary conditions.