Study On Dynamic Response Of Orthotropic Membranes Under Impact Loading

Along with the Society development and technology never give up advancement. The membrane structure was used wildly in many fields. In the architecture field, the application of tensioned membrane structure was the most extensive in all kinds of membrane structure systems, the stiffness of which was formed by applying pretension to it. In order to control the actual pretension value tally with the design pretension value, prevent the fold, relaxation and the adverse effects of wind vibration, reduce the engineering accidents, the accurate measurement of the membrane structure's pretension seems very important and necessary. This article based on the new method of measuring the membrane structure's pretension named"ejection method". This method assumes a small ball which is regarded as a particle eject onto a tensioned membrane surface with edges fixed, then the tensioned membrane vibrate and the small ball was rebounded. Through measuring the small ball's ejection velocity and rebound velocity, the membrane's pretension can be obtained. The mechanical behavior during the process and the error influence of membrane surface size obtained through the research on the dynamic response of the membrane under impact loading can provide a theoretical foundation in the development of the survey eauipment. Oterwise, the membrane structure is very sensitive to wind, rain, hail. So it will easily to vibrate under impact of them. The research on the dynamic response is particularly important to the membrane structure design and normal construction.The velocity ball impact membrane surface is used as the impact loading model to simulate the process in this article. Firstly , the large deflection theory of membrane was applied to research the vibration of orthotropic rectangle and circular membrane with the initial deflections. Derived the governing vibration equations of orthotropic membrane, and obtained the power series formula of nonlinear vibration frequency of rectangular membrane with edges fixed. Then the mathematical model is developed for the membrane under impact loading. The basic equations of forced vibration for the orthotropic membrane was formulated based on the governing vibration equations of orthotropic membrane, Decompose the displacement function and stress function by fourier series and put it into the basic equations, neglect the the singular stress in membrane, and obtained the dynamic governing equations. solved it by the Lindstedt PoincaréPerturbation Method. and obtained the formula of impact load and nonlinear forced vibration deflection of rectangular membranes with edges fixed. Then a numerical computation method for the equation is used. Finally, Numerical simulations confirm the results of the theoretical analysis.During the process of membrane's vibration, difference between the mathematical simulation of the membrane's deflection and the real vibration modes would cause errors. The article analyses the effect of membrane surface size on the error through actual examples combined with the finite element numerical methods. And then the different initial conditions and and material parameters which influence the performance of membrane's vibration are discussed, obtained the general regularity with the variation of the above-mentioned factors. These conclusions can provide theoretical basis for the dynamical analysis of membrane andr the developing of the"ejection method"measuring instruments and membrane structure's design and construction.