温室风振分析中的压杆弯曲振动动态刚度阵模型

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

关键词:  温室  风振  压杆，弯曲振动  二阶效应  刚度矩阵法

Key words:  greenhouse  wind vibration  compression bar  flexural vibration  second-order effect  stiffness matrix method

摘要:

为研究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几何方程、平衡方程和物理方程，建立了压杆横向弯曲振动微分方程，得到了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，求得了以节点位移向量表达的位移系数，给出了压杆截面内力方程，进而得到了以节点位移向量表达的杆端内力，最终给出了综合质量矩阵、几何矩阵和刚度矩阵的动态刚度矩阵。该方法可获得用矩阵、向量格式表达的压杆弯曲振动分析的精确解，计算简单方便，适用于风荷载作用下温室中压杆的动力性能及动力响应的精确求解。

Abstract:

In order to research the flexural vibration of compression bar in greenhouse wind vibration analysis, differential equation for transverse flexural vibration of compression bar was constructed according to geometric equation, equilibrium equation and physics equation 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 was 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 can provide an exact solution for flexural vibration of compression bar expressed in matrix and vector format, which is simple and useful. And it can be applied to accurate analysis for dynamic performance and dynamic responses of compression bar in greenhouse under wind load.