伞形膜结构在冰雹荷载作用下的非线性动力响应

对伞形张拉膜结构在自然灾害等外荷载冲击下的振动反应进行研究，为实际工程膜结构建筑受灾破坏分析提供依据。基于冯·卡门大挠度理论和薄板振动理论，建立伞形张拉膜结构在冰雹荷载作用下的非线性动力响应控制方程。采用贝塞尔函数及欧拉方程求得其振型函数，再运用KBM摄动法和迦辽金法对控制方程求解，得到其动力响应的近似解析解。利用Mathmatics软件对方程进行求解并对求解后的数据进行整理，通过Origin绘图软件画出膜面受迫振动后的时程位移图。采用ANSYS软件建立伞形张拉膜结构的有限元模型；再通过LS-DYNA显示动力学模块对冰雹冲击膜面的动力过程进行模拟，得到膜面动力响应的结果。同理，画出数值模拟结果的位移图，将整理后的理论与数值分析数据结果进行对比分析，结果表明，理论解析和数值分析结果吻合。

Nonlinear dynamic response of umbrella membrane structure under hail load

This paper investigates the vibration response of umbrella shaped tensioned membrane structure under the impact of natural disasters and other external loadings, and provides the basis for the damage analysis of actual membrane structures. Based on von Karman''s large deflection theory and thin plate vibration theory, the nonlinear dynamic response control equation of umbrella shaped tensioned membrane structure under hail load is established. Bessel function and Euler equation are used to obtain the mode function, and KBM perturbation method and Galerkin method are used to solve the governing equation to obtain the approximate analytical solution of its dynamic response. The equations are solved by Mathematics software, and the data are sorted out. The time history displacement diagram of membrane surface after forced vibration is drawn by Origin drawing software. ANSYS software is used to establish the finite element model of umbrella shaped membrane structure; then, the dynamic process of hail impacting on the film surface is simulated by LS-DYNA display dynamics module, and the dynamic response of the film surface is obtained. In the same way, the displacement diagram is plotted, and the data results of the sorted theory and numerical analysis are compared and analyzed. The results show that the theoretical and numerical results are more consistent.