Theoretical and Numerical Studies on Damped Nonlinear Vibration of Orthotropic Saddle Membrane Structures Excited by Hailstone Impact Load

Abstract

The orthotropic membrane structures have been popular in architectural structures. However, because of its lightweight and small stiffness, large nonlinear deflection vibration may occur under impact load, which leads to structural failure. In this paper, the governing equations of the large deflection nonlinear damped vibration of orthotropic saddle membrane structures excited by hailstone impact load are proposed according to the von Kármán’s large deflection theory and solved by applying the Bubnov–Galerkin method and the method of KBM perturbation. The approximate theoretical solution of the frequency function and displacement function of the large deflection nonlinear damped vibration of saddle membrane structures with four edges fixed excited by hailstone impact was obtained. The analytical examples proved that the mode shape function (equation (43)) can be applied to calculate the single-order mode shapes and the total superposed mode shapes of the damped large nonlinear deflection vibration of orthotropic saddle membrane structures excited by hailstone impact load succinctly. In addition, we compare and analyze the results of vibration frequency, amplitude, time histories, and total displacement of membrane structures with different pretensions and arch-to-span ratios under the impact of differently sized hailstones. The correctness of the analytical theory is verified by comparing with the results of numerical simulation. According to the results of this paper, we put forward some suggestions for the vibration control and dynamic design of practical spatial membrane structures.