温室风振分析中的压杆弯曲振动动态刚度阵模型

针对温室风振分析中的压杆弯曲振动问题,根据考虑二阶效应和惯性力影响的压杆基本方程建立压杆横向弯曲振动微分方程,得到采用基函数和位移系数表达的压杆横向弯曲振动位移的向量表达式,结合位移边界条件求得以节点位移向量表达的位移系数,给出压杆截面内力方程,进而得到以节点位移向量表达的杆端内力,最终给出综合质量矩阵、几何矩阵和刚度矩阵的精确动态刚度矩阵。研究结果表明:一般的插值形函数单元模型需加密单元才能提高计算精度,但仍存在误差,而本研究模型得到的压杆横向弯曲自振圆频率与解析法计算获得的理论解完全相同,为精确解。

Dynamic stiffness matrix model for the flexural vibration of compression bar in greenhouse wind vibration analysis

Aiming at the problem of flexural vibration of compression bar in greenhouse wind vibration analysis, differential equation for transverse flexural vibration of compression bar was designed according to fundamental equations of compression bar considering its second-order effect and inertia force. Displacement vector expressed by the basis function and the displacement coefficient for transverse flexural vibration of compression bar were also achieved. Based on the displacement boundary condition, displacement coefficient expressed by nodal displacement vector was obtained. Internal force equations of compression bar were established and then internal force at bar ends expressed by nodal displacement vector was provided. Finally, total dynamic stiffness matrix colligating mass matrix, geometry matrix and stiffness matrix was given. This method provided exact solution for the flexural vibration of compression bar expressed in matrix and vector format, which was simple and useful. When use the interpolation function unit model, dividing the unit more densely could improve the accuracy of the calculation, but there were still errors. The results showed that the angular frequency of the transverse bending of compression bar obtained by the study model was the exact solution, which was exactly the same as the theoretical solution obtained by the analytical method.