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基于动力刚度法和有限元理论提出了一种考虑二阶效应计算梁杆动力响应的新方法。通过求解轴向力作用下Bernoulli-Euler梁横向和轴向挠度自由振动微分方程,利用位移边界条件反解出待定系数,得到了动态精确形函数;使用经典有限元方法推导了考虑截面自身旋转惯量的质量阵和考虑二阶效应的刚度阵,该质量阵和刚度阵各元素均为轴力和圆频率的超越函数;建立了杆系结构瞬态动力学分析的动力平衡方程,给出了稳定和高效的求解方案。对几个典型的算例进行了计算分析,并与通用软件ANSYS的计算结果进行了比较。计算结果表明:该分析梁杆系统动力响应的新方法具有较高的计算精度和效率,特别是能够准确地计入轴力对于梁杆动力响应的影响。
Based on dynamic stiffness method and finite element theory, a new method to calculate the dynamic response of the beam considering the second order effect is proposed. By solving the free-vibration differential equations of the Bernoulli-Euler beam under axial force, the undetermined coefficients of the Bernoulli-Euler beam are inversely solved by displacement boundary conditions, and the dynamic exact shape function is obtained. The classical finite element method And the stiffness matrix considering the second order effect. The elements of the mass matrix and the stiffness matrix are the transcendental functions of the axial force and the circular frequency. The dynamic balance equation of the transient dynamic analysis of the rod structure is established, and the stability And efficient solution. Several typical examples are calculated and analyzed, and compared with the results of the general software ANSYS. The calculation results show that the new method for analyzing the dynamic response of the beam system has higher calculation accuracy and efficiency, especially the influence of axial force on the dynamic response of the beam.