Random vibration of pretensioned rectangular membrane structures under heavy rainfall excitation

Abstract

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.