Large amplitude flexural vibration of simply supported skew plates.
01 Sep 1973-AIAA Journal (American Institute of Aeronautics and Astronautics Inc. (AIAA))-Vol. 11, Iss: 9, pp 1279-1282
TL;DR: In this article, the Berger formulation was applied to the large amplitude flexural vibration of orthotropic skew plates in the Berger regime and the results were compared with those obtained without making use of the approximate formulation due to Berger.
Abstract: Using the governing dynamic equations for the large amplitude flexural vibration of orthotropic skew plates in the Berger formulation, solutions are obtained on the basis of a one term vibration mode and they are discussed for two types of in-plane edge conditions and for different skew angles and orthotropy. The results obtained are compared with those got without making use of the approximate formulation due to Berger. In all these cases it is found that the nonlinearity is of the hardening type, i.e., the period of nonlinear vibration decreases with increasing amplitude.
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TL;DR: In this article, a non-linear analysis of plate and shell structures under mechanical and thermal loading is presented, with the inclusion of curvature for a skew rectangular panel to analyze thermal stresses for movable edge boundary condition.
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TL;DR: In this article, simplified equations for the deflection of uniformly loaded circular and rectangular plates with various boundary conditions are derived and compared with available numerical solutions of the exact equations, and the deflections found by this approach are then used to obtain the stresses, and resulting stresses are compared with existing solutions.
Abstract: As a result of the assumption that the strain energy due to the second invariant of the middle surface strains can be neglected when deriving the differential equations for a flat plate with large deflections, simplified equations are derived that can be solved readily. Computations using the solution of these simplified equations are carried out for the deflection of uniformly loaded circular and rectangular plates with various boundary conditions. Comparisons are made with available numerical solutions of the exact equations. The deflections found by this approach are then used to obtain the stresses, and the resulting stresses are compared with existing solutions. In all the cases where comparisons could be made, the deflections and stresses agree with the exact solutions within the accuracy required for engineering purposes.
441 citations
TL;DR: In this paper, approximate solutions for the nonlinear bending vibrations of thin plates are presented for the cases of rectangular and circular plates subjected to various boundary conditions, and the effects of large amplitudes on both the free and forced vibrations are clarified.
Abstract: Approximate solutions for the nonlinear bending vibrations of thin plates are presented for the cases of rectangular and circular plates subjected to various boundary conditions, and the effects of large amplitudes on both the free and forced vibrations are clarified
263 citations
TL;DR: By using an approximate formulation due to Berger, it was shown that the vibration of rectangular plates with large amplitudes may be treated in a simple and unified manner as mentioned in this paper, and numerical results were given for various boundary conditions.
108 citations
TL;DR: In this article, the Von Karman field equations for flexible oblique plates with an initial curvature are extended to a dynamical case using series of initial and additional deflections and Galerkin's procedure, the governing equation for an admissible mode time function is established using this single assumed modal deflection, and assuming built-in edge fiee to move in the inplane directions.
Abstract: Von Karman field equations for flexible oblique plates with an initial curvature are extended to a dynamical case Using series iepresentation of initial and additional deflections and Galerkin's procedure, the governing equation for an admissible mode time function is established Using this single assumed modal deflection, and assuming built-in edge fiee to move in the inplane directions, the following particular cases are discussed: buckling of an oblique plate under uniaxial compressive load, free linear vibrations of a square plate, large deflections of a uniformly loaded square plate, snap-through phenomena of a curved oblique plate under uniform transverse load, and free nonlinear vibrations A numeiical example concerning a rhombic plate is discussed in more detail The well-known fact of a decrease of the period of nonlinear vibrations with an increasing amplitude is corroborated, this relation being less pronounced for larger sweep angles
20 citations
TL;DR: In this article, the large amplitude (non-linear) free flexural vibration of thin, elastic, orthotropic skew plates clamped along all four edges was analyzed using the Galerkin's method.
15 citations