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Öğe Buckling and vibration of non-ideal simply supported rectangular isotropic plates(Pergamon-Elsevier Science Ltd, 2006) Aydogdu, M; Ece, MCBuckling and vibration of a rectangular isotropic plate which has non-ideal simply supported boundary conditions along one of its edges are investigated. It is assumed that one of the edges of the plate allows a small non-zero deflection and a small non-zero moment. Externally applied in-plane loads are considered to be parallel and perpendicular to the edge where non-ideal boundary conditions are present in the buckling problem. Analytical solutions of the buckling and vibration problems are obtained by using the Linshtead-Poincare perturbation technique. Improved buckling loads and natural frequencies are determined for various values of the aspect ratio of the plate. (C) 2005 Elsevier Ltd. All rights reserved.Öğe Buckling of symmetric cross-ply square plates with various boundary conditions(Elsevier Sci Ltd, 2005) Timarci, T; Aydogdu, MThe buckling analysis of cross-ply laminated square plates subjected to three types of in-plane forces and various edge boundary conditions is presented on the basis of a unified five-degree-of-freedom shear deformable plate theory. The employment of the appropriate shear deformation shape functions in the theory leads to certain shear deformable plate theories developed previously, also, fulfills the requirement of the continuity conditions among the layers. The governing equations of buckling behaviour of completely simply supported cross-ply laminated plates are solved analytically. For the plates with different combinations of free, clamped and simply supported boundary conditions at their edges, the Ritz method is applied by assuming the displacement components as the double series of simple algebraic polynomials. The numerical results obtained on the basis of various plate theories for uniaxial, biaxial compression and compression-tension types of loading and different length-to-thickness ratios are presented and compared with the ones available in the literature. (c) 2004 Elsevier Ltd. All rights reserved.Öğe Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method(Pergamon-Elsevier Science Ltd, 2005) Aydogdu, MThe present study is concerned with the vibration analysis of cross-ply laminated beams subjected to different sets of boundary conditions. The analysis is based on a three-degree-of-freedom shear deformable beam theory. The continuity conditions between layers of symmetric cross-ply laminated beams are satisfied by the use of the shape function incorporated into the theory which also unifies the ID shear deformable beam theories developed previously. The governing equations are obtained by means of Hamilton's principle. Six different combinations of free, clamped and simply supported edge boundary conditions are considered. The free vibration frequencies are obtained by applying the Ritz method where the three displacement components are expressed in a series of simple algebraic polynomials. The numerical results obtained for different length-to-thickness ratios and lay-ups are presented and compared with results available in the literature. (c) 2005 Elsevier Ltd. All rights reserved.Öğe Vibration analysis of cross-ply laminated square plates with general boundary conditions(Elsevier Sci Ltd, 2003) Aydogdu, M; Timarci, TThis study is concerned with the vibration analysis of cross-ply laminated square plates subjected to different sets of boundary conditions. The analysis is based on a five-degree-of-freedom shear deformable plate theory. The requirement of the continuity conditions among the layers for the symmetric cross-ply laminated plates are fulfilled by the use of the shape functions incorporated into this theory which, also, unifies the two-dimensional shear deformable plate theories developed previously. Initially, the governing equations obtained by use of Hamilton's principle for the vibration of cross-ply laminated plates with simply supported boundary conditions at all of their edges are solved by an exact analytical method. In the case of cross-ply laminated square plates subjected to twelve different combinations of free, clamped and simply supported edge boundary conditions, the free vibration frequencies are obtained by applying the Ritz method where the five displacement components are assummed as the series of simple algebraic polynomials. The numerical results obtained for different length-to-thickness ratios and material arrangements are presented and compared with the ones available in the literature. (C) 2003 Elsevier Science Ltd. All rights reserved.
