Random vibration of composite saddle membrane structure under the impact loading

Abstract

Large-span composite membrane structure is light in weight and small in stiffness, which may produce violent random vibration under the random impact, such as wind, rain, hail and windborne debris. In order to accurately understand the random vibration response of membrane structure, the dynamics of composite saddle membrane structure under the stochastic impact load is studied in this paper. The governing equation of random vibration is established based on the von Karman large deflection theory of thin shell and the shallow membrane assumption. The orthotropy, damping and geometrical nonlinearity are considered for the composite membrane. The stochastic pulse of the impact load is imposed based on the statistical data of impact velocity difference. The perturbation method is used to solve the stochastic vibration equation, and the statistical moments of the displacement are derived from the Galerkin method, which is then validated against the numerical simulations. The comparison shows that the analytical solution can well predict the random dynamic response of saddle membrane structure under the impact load. Finally, it is discovered by the parametric studies that the average displacement reduces with the increase of membrane pretension and arch span ratio, and grows with the increase of impact velocity difference.