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This paper is concerned with the nonlinear damped forced vibration problem of pre-stressed orthotropic membrane structure under impact loading. The governing equations of motion were derived based on the von Kármán large deflection theory and D'Alembert's principle, and solved by using the Bubnov–Galerkin method and the Krylov–Bogolubov–Mitropolsky (KBM) perturbation method. The asymptotic analytical solutions of the frequency and lateral displacement of rectangular orthotropic membrane with fixed edges were obtained. In the computational example, the frequency results were compared and analyzed. Meanwhile, the vibration mode of the membrane and the displacement and time curves of each feature point on the membrane surface were analyzed. The results obtained herein provide a simple and convenient approach to calculate the frequency and lateral displacement of the nonlinear forced vibration of rectangular orthotropic membranes with low viscous damping under impact loading. In addition, the results provide some computational basis for the vibration control and dynamic design of membrane structures.

This paper studies the calculation method about the displacement response mean function of rectangular orthotropic membranes with four edges fixed under stochastic impact loading. We set up the nonlinear stochastic governing differential equation, solve it according to the perturbation method and the random vibration theory and obtain the displacement response mean value function of the membrane surface. Furthermore, this paper makes a random simulation test for ZZF membrane material which is commonly applied in the membrane structural engineering and obtains abundant deflection response sample curves about the feature points of the membrane surface. For sample curves statistical analysis at some fixed time, sample means can be obtained, which verify the correctness of the theoretical calculation method. The calculation method provides a theoretical basis for vibration control of building membrane structures to control the occurrence of natural disasters.

An exact solution to the bending of variable-thickness orthotropic plates is developed for a variety of boundary conditions. The procedure, based on a Lévy-type solution considered in conjunction with the state-space concept, is applicable to inhomogeneous variable-thickness rectangular plates with two opposite edges simply supported. The remaining ones are subjected to a combination of clamped, simply supported, and free boundary conditions, and between these two edges the plate may have varying thickness. The procedure is valuable in view of the fact that tables of deflections and stresses cannot be presented for inhomogeneous variable-thickness plates as for isotropic homogeneous plates even for commonly encountered loads because the results depend on the inhomogeneity coefficient and the orthotropic material properties instead of a single flexural rigidity. Benchmark numerical results, useful for the validation or otherwise of approximate solutions, are tabulated. The influences of the degree of inhomogeneity, aspect ratio, thickness parameter, and the degree of nonuniformity on the deflections and stresses are investigated.