This paper analytically and experimentally investigates the random vibration problem of pretensioned rectangular membrane structures under heavy rainfall. An analytical model is firstly proposed. In this model, the heavy rainfall is modeled as a series of discretized pulse load whose amplitude follows the non-Gaussian distribution; then, the nonlinear governing equation and corresponding Fokker Planck Kolmogorov (FPK) equation of membrane structures are derived and solved by the perturbation method, considering both the geometrical nonlinearity of structure and the non-Gaussian type of load; consequently, the analytical solutions of the probability density function (PDF), mean and standard deviation of displacement response can be obtained. An artificial heavy rainfall experimental system is then developed. This system is used to (i) verify the analytical model and (ii) evaluate the effects of rainfall intensity, pretension level, and material properties. The results show that the displacement follows the significant non-Gaussian distribution and proves strong nonlinear characteristics with increasing rainfall intensity and pretension. The proposed analytical model can guide engineers to design membrane structures from the perspective of probability.

本文通过分析和实验研究了强降雨条件下预张矩形膜结构的随机振动问题。首先提出了一种分析模型。在该模型中，暴雨被建模为一系列离散的脉冲负载，其幅度遵循非高斯分布。然后，考虑结构的几何非线性和非高斯类型的荷载，通过摄动法推导并求解了膜结构的非线性控制方程和相应的Fokker Planck Kolmogorov（FPK）方程。因此，可以获得位移响应的概率密度函数（PDF），均值和标准差的解析解。然后开发了人工强降雨实验系统。该系统用于（i）验证分析模型和（ii）评估降雨强度，预应力水平和材料特性的影响。结果表明，位移遵循显着的非高斯分布，并且随着降雨强度和预应力的增加而表现出强烈的非线性特征。所提出的分析模型可以指导工程师从概率角度设计膜结构。