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

Abstract

The orthotropic <?tex id="Q1" staff-cmt="It is very important for the corresponding author to have a linked ORCID (Open Researcher and Contributor ID) account on MTS. To register a linked ORCID account, please go to the Account Update page (http://mts.hindawi.com/update/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.

Experimental and numerical investigation on dynamic responses of the umbrella membrane structure excited by heavy rainfall

“…Thus, the membrane structure is prone to large vibrations under dynamic load of wind or rainfall, which goes against the structural stability and even leads to structural failures (Liu et al, 2019a). At present, research studies on the dynamic response of membrane structures mainly focus on the analytical solution of vibration of planar membrane structures and the coupling problem of space membrane structures under wind loads (Liu et al, 2019b). And, few studies have been conducted on the effect of heavy rainfall load on membrane structures.…”

Hailstone-induced dynamic responses of pretensioned umbrella membrane structure

“…Zhu and Yang (2010) investigated the saddle membrane structure response under the actions of wind-structure coupling and wind-rain coupling by means of finite element method. Liu et al (2019b) studied the large deflection nonlinear damped vibration of orthotropic saddle membrane structures excited by hailstone impact load by analytical and numerical methods. Hincz and Gamboa-Marrufo (2016) and Yu et al (2005) investigated the pressure coefficients of tensile umbrella membrane structures subjected to wind loads by wind tunnel test.…”