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In this study, the nonlinear vibration of a sandwich FG plate resting on a nonlinear Pasternak foundation which is simultaneously subjected to transverse harmonic forcing excitation and in-plane static force is investigated. Based on the Modified First-Order Shear Deformation Theory (FSDT), applying the von-Karman nonlinear strain–displacement relation and the Hamilton’s principle, the governing nonlinear coupled partial differential equations are derived. Then, the Galerkin’s procedure is used to reduce the equations of motion to nonlinear ordinary differential equations. In the absence of foundation, the validity of the formulation for analyzing the modified shear correction factors for shear stresses is accomplished by comparing the results with those reported in the literature. By applying the multiple scales method and considering the second order nonlinear approximation of solution, the primary resonance of the system under the transverse forcing excitation is analyzed. Under the steady-state condition, the frequency-response, the force-response and the damping-response equations are derived. Then the conditions of existence and stability of multiple coexisting non-trivial solutions for amplitude of the responses are discussed and the saddle node bifurcation points of the characteristic curves are derived. It is shown that, the variation of the system parameters in the resonance boundary may cause the jump phenomenon. Moreover, the effects of the system parameters including, excitation frequency, foundation parameters, damping, and amplitude of the harmonic and in-plane forces on the system nonlinear dynamics are investigated. Also it is shown that the presence of the foundation has a considerable influence on the resonance characteristic curves.

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Because of the continuous changes of mechanical properties of functionally graded materials and therefore reducing the effects of stress concentration, many researchers are interested in studying the behavior and use of these materials in various industries. For the correct design of perforated inhomogeneous plate is needed to know the accurate information about the deformation and stress distribution in different points of the plate especially around the hole. In this paper, is tried to present the analytical solution to calculate the 2D stress distribution around the circular hole in long FG plate, by using the complex potential functions method. The plate subjected to constant uniaxial or biaxial stress. One of the most important goal of this research is to study the effect of compression load applied to the hole boundary on stress distribution around the hole. The variation of material properties, especially Young's modulus is in a radial direction and concentric to the hole. The special exponential function is used to describe the variation of mechanical properties. The finite element method has been used to check the accuracy of analytical results for homogeneous and heterogeneous plates, also for all loading cases. In the presence of applied load at the boundary of circular hole, amount of radial stress in addition to hoop stress is considerable. Therefore the Von Mises stress is used to study the stress around the hole. The results showed that inhomogeneous plate with increased modulus of elasticity has greater load bearing capacity with respect to homogeneous plate.