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In this paper, the governing equations for a vibratory beam with moderately large deflection are derived using the first order shear deformation theory. These equations which are a system of nonlinear partial differential equations with constant coefficients are solved analytically with the perturbation technique and the natural frequencies and the buckling load of the system are determined. A parametric study is performed and the effects of the geometrical and material properties on the natural frequency and buckling load are investigated and the effect of normal transverse strain and axial load on natural frequency are examined. Some results based on the first order shear deformation theory are consistent with classic theories of beams and some yield different results. Formulation presented to calculate the transverse frequency, determines the axial frequency too. Also, the natural frequencies and buckling load are calculated with the finite elements method by applying one and three-dimensional elements and the results are compared with the analytical solution.

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In this paper, the buckling of rectangular plates subjected to non-uniform in-plane loading is investigated. At first the equilibrium equations of plate based on the first order shear deformation theory have been extracted. The kinematic relations have been assumed based on the von-Karman model and the Hook’s law has been considered as the constitutive equations. The adjacent equilibrium method has been used for deriving the stability equations. The equilibrium equations which are related to the prebuckling stress distribution, have been solved using the differential equations theory. To determine the buckling load of a simply supported plate, the Galerkin method has been used for solving the stability equations which are a system of differential equations with variable coefficients. In this paper, four types of in-plane loading, including the uniform, parabolic, cosine and triangular loading, have been considered and the effects of the plate aspect ratio and thickness on the buckling load has been investigated and the results have been compared with the finite element method and the classical plate theory. The comparison of the results show that for all loading cases, the buckling load computed by the classical plate theory is higher than the value obtained based on first order shear deformation theory.

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Glass-reinforced phenolic laminates show a low resistance to delamination. Toughening of the matrix resin with a polymeric interlayer is among the method used to improve the delamination strength. In this research Polyvinyl butyral(PVB) nanoweb with the fiber diameter of 300-600 nanometer were used as an interlayer in a 14-layer glass reinforced phenolic composite. A hybrid nanoweb consists of PVB nanoweb reinforced with pyrolytic carbon and carbon nanotube (CNT) were also prepared and used as the interlayer. Mode I and Mode II delamination tests were conducted on the samples according to the related ASTM standard test method. The results showed that PVB interlayer improves the delamination strength of the composites by 13.6% and 13.8%. for mode I and Mode II, respectively. Also, with the hybrid nanoweb, better improvement in the fracture toughness was achieved. In the hybrid nanowebs, CNTs at the optimum amount has a greater effect on the Mode I fracture (49% improvement in GIc), while the pyrolytic carbon mainly affected the Mode II fracture toughness by 38% improvement in GIIc. Morphological studies carried out by SEM microscopy showed that crack deviation is the dominant mechanism for toughening of the polymeric matrix which results in the delay in fracture initiation and increase of the crack length and in doing so enhances the fracture toughness of the laminates.