基于几何非线性圆拱动力模型的拱形温室自振周期分析

针对拱形温室结构动力分析中的杆件弯曲振动问题,采用直接刚度法,对拱形温室自振特性进行研究。在分析拱的弯曲变形、剪切变形、轴向压缩变形、二阶效应以及基于分布质量的平动惯性力和转动惯性力的基础上,建立了圆拱的位移控制方程,求解得到了非线性平转动Timoshenko圆拱动力模型。由定解条件,得到了特征方程,通过求解特征方程,给出了拱形温室自振周期的计算方法。利用本研究模型及其退化模型,计算了拱棚和典型拱形温室结构在不同模型下的自振周期,分析了不同模型的计算结果,分析表明,本研究建立的几何非线性可压缩平转动Euler梁模型可用于拱形温室结构自振周期计算。

Analysis of natural vibration period of arch greenhouse based on a geometric nonlinear dynamic model of circular arch

Aiming at the bending vibration problem of bar in dynamic analysis of arch greenhouse structure, the natural vibration characteristics of arch greenhouse were studied by direct stiffness method. Based on the analysis of bending deformation, shear deformation, axial compression deformation, second-order effect and translational inertia force and rotational inertia force based on distributed mass, the displacement control equation of circular arch is established, and the nonlinear translational Timoshenko circular arch dynamic model is obtained. The characteristic equation is obtained by the definite solution condition. By solving the characteristic equation, the calculation method of natural vibration period of arched greenhouse is given. By using the model established in this study and its degradation model, the natural vibration periods of arch shed and typical arched greenhouse structure under different models are calculated, and the calculation results of different models are analyzed. In conclusion, the geometric nonlinear compressible flat rotation Euler beam model established in this study can be used to calculate the natural vibration period of arched greenhouse structure.