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Journal ArticleDOI

Nonlinear Vibration of Elastic Skew Plates Exhibiting Rectilinear Orthotropy

TL;DR: In this article, the authors derived the governing equations for large amplitude flexural vibrations of orthotropic skew plates from the corresponding static equations derived in this paper, making use of an approximation originally due to Berger, corresponding simplified equations are also derived.
Abstract: The governing equations for large amplitude flexural vibrations of orthotropic skew plates are obtained from the corresponding static equations derived in this paper. Making use of an approximation originally due to Berger, corresponding simplified equations are also derived. Considering the large amplitude free flexural vibration of orthotropic skew plates clamped along all the edges, it is shown that the Berger approximation leads to results good enough for engineering purposes. Amplitude vs period curves are presented for different aspect ratios and skew angles of the plate under two in-plane edge conditions. It is observed that the amplitude vs period behaviour is of the hardening type, i.e. period decreases with increasing amplitude.
Citations
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Journal ArticleDOI
TL;DR: In this paper, a nonlinear free vibration analysis of thin-to-moderately thick laminated composite skew plates is presented based on the first order shear deformation theory (FSDT) using differential quadrature method (DQM).

75 citations

Journal ArticleDOI
TL;DR: Using a differential quadrature (DQ) method, large amplitude free vibration analysis of laminated composite skew thin plates is presented in this paper, where the governing equations are based on the thin plate theory (TPT) and the geometrical nonlinearity is modeled using Green's strain in conjunction with von Karman assumptions.
Abstract: Using a differential quadrature (DQ) method, large amplitude free vibration analysis of laminated composite skew thin plates is presented The governing equations are based on the thin plate theory (TPT) and the geometrical nonlinearity is modeled using Green's strain in conjunction with von Karman assumptions To cause the impact due to nonlinear terms more significant, in-plane immovable simply supported, clamped and different combinations of them are considered The effects of different parameters on the convergence and accuracy of the method are studied The resulted solutions are compared to those from other numerical methods to show the accuracy of the method Some new results for laminated composite skew plates with different mixed boundary conditions are presented and are compared with those obtained using the first order shear deformation theory based DQ (FSDT-DQ) method Excellent agreements exist between the solutions of the two approaches but with much lower computational efforts of the present DQ methodology with respect to FSDT-DQ method

67 citations

Journal ArticleDOI
TL;DR: In this paper, the effects of various parameters on the non-linear vibration frequencies of a simply supported rectangular moderately thick plate subjected to initial stress is investigated. But the effects on the frequency of the flexural vibration were not considered.

53 citations

Journal ArticleDOI
TL;DR: In this article, the effects of transverse shear and rotatory inertia on the flexural vibration of elastic, isotropic skew plates were investigated and the influence of these effects on aspect ratios and skew angles of thin and moderately thick skew plates was investigated both at small and large amplitudes.

23 citations

Journal ArticleDOI
TL;DR: In this article, the large amplitude free flexural vibrations of thin, elastic anisotropic skew plates are studied by using the von Karman field equations in which the governing non-linear dynamic equations are derived in terms of the stress function and the lateral displacement.

14 citations

References
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Journal ArticleDOI
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

Book
01 Jan 1963

272 citations

Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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