基于Rayleigh-Ritz法的考虑配重位置影响的固支圆弧拱平面外自振频率计算

Calculation of the Out-of-Plane Natural Frequencies of Fixed Circular Arches with Additional Weight Adhered Based on Rayleigh-Ritz Method

拱结构在服役期间,拱上的不同位置必然会承受重物,为了探究拱上任意位置配重对拱面外振动频率的影响,利用Rayleigh-Ritz法建立考虑任意位置配重作用下两端固支圆弧拱的面外自振频率方程,通过特征值求解的方法得到了其自振频率。利用ANSYS软件,建立了相应的有限元模型进行数值模拟,结果显示理论计算频率和数值计算频率吻合良好,验证了本文理论方法的正确性。在此基础上,通过参数分析讨论了配重大小、配重作用位置和圆心角对拱的面外自振频率的影响,计算结果表明,在拱上增加配重会使其面外自振频率减小,而随着配重作用位置偏离拱顶越远,拱的面外自振频率则越大,同时参数分析还表明拱的自振频率随着圆心角的增大而减小。

There is additional weight on the arch during its service time. In order to investigate the effect of additional weight on the out-of-plane natural frequencies of fixed circular arches,the analytical solution for the natural frequency of arch with additional weight located at different position is derived using the principle of stationary mechanical energy in conjunction with the Rayleigh-Ritz method. By solving the eigenvalue problem given by the frequency equation,analytical natural frequencies of arch are obtained. The analytical solutions are compared with the FE results of ANSYS model and the results agree well with each other which indicates the accuracy of the analytical method is great. The validated finite element model is used to conduct further parametric studies for effects of different parameters such as value of additional weight,position of additional weight and central angle of arch on the outof-plane natural frequencies of fixed circular arches. It is found that the natural frequency of the arch is decreasing as the value of additional weight increasing,and the natural frequency of arch is also increasing as the additional weight location moving from the arch crown to the arch ends. It is also found that as the central angle of arch increasing the natural frequency of arch is decreasing.