Abstract
The orthotropichttp://mts.hindawi.com/update/) in our Manuscript Tracking System and after you have logged in click on the ORCID link at the top of the page. This link will take you to the ORCID website where you will be able to create an account for yourself. Once you have done so, your new ORCID will be saved in our Manuscript Tracking System automatically."?>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.
Highlights
Academic Editor: Davood Younesian e orthotropic membrane structures have been popular in architectural structures
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 Karman’s large deflection theory and solved by applying the Bubnov–Galerkin method and the method of Krylov–Bogolubov– Mitropolsky (KBM) perturbation. e 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. e 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
The approximate formulas of hailstone terminal velocity were substituted into the governing equations of the large deflection nonlinear damped vibration of orthotropic saddle membrane structures excited by impact load
Summary
We study a saddle, namely, hyperbolic paraboloid, membrane structure with four edges supported under an impact load. e theoretical model of saddle membrane structure is shown in Figure 1. e orthogonal axes x and y are the two different Young’s modulus fiber directions of orthotropic saddle membrane structures. a and b, respectively, are the spans in x and y axes. We study a saddle, namely, hyperbolic paraboloid, membrane structure with four edges supported under an impact load. E orthogonal axes x and y are the two different Young’s modulus fiber directions of orthotropic saddle membrane structures. A and b, respectively, are the spans in x and y axes. N0x and N0y, respectively, denote the pretension in x and y axes. F1 and f2, respectively, are the midspan arch in x and y axes. E sphere H is a hailstone; v0 denotes the velocity of the hailstone; (x0, y0) is the impact point on membrane surface. Where z0 denotes the initial surface function of saddle membrane structure. According to equation (1), the two initial principal curvatures in x and y directions are. With the action of the pretensions N0x and N0y [28], we can obtain k0xN0x + k0yN0y 0
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