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Journal ArticleDOI

Vibration of simply supported-clamped skew plates at large amplitudest

08 Mar 1973-Journal of Sound and Vibration (Academic Press)-Vol. 27, Iss: 1, pp 37-46
TL;DR: In this paper, the relationship between the amplitude and period of orthotropic skew plates for various aspect ratios and skew angles under two in-plane edge conditions is investigated and the validity of the Berger approximation is investigated for the problem under consideration.
About: This article is published in Journal of Sound and Vibration.The article was published on 1973-03-08. It has received 6 citations till now. The article focuses on the topics: Skew & Orthotropic material.
Citations
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Journal ArticleDOI
TL;DR: Zhou et al. as discussed by the authors employed the moving least square technique to establish the trial function for the transverse displacement of a skew plate and the Ritz method was applied to derive the governing eigenvalue equation for the skew plate.

53 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

Journal ArticleDOI
TL;DR: In this paper, the effect of boundary condition nonlinearities on free nonlinear vibrations of thin rectangular plates is analyzed and the results of the calculations with nonlinear boundary conditions differ essentially from the data obtained without these boundary conditions.
Abstract: The effect of boundary condition nonlinearities on free nonlinear vibrations of thin rectangular plates is analyzed. The method for analysis of the plate vibrations with geometrical nonlinearity and the boundary condition nonlinearity is suggested. The nonlinear boundary conditions for membrane forces are transformed into linear ones using the in-plane stress function. Additional boundary conditions for the in-plane displacements vanishing on the clamped edge of the plate are imposed on the stress function. Simply supported and cantilever plates are analyzed. The backbone curves obtained by satisfying linear and nonlinear boundary conditions are compared. It is shown that the results of the calculations with nonlinear boundary conditions differ essentially from the data obtained without these boundary conditions.

11 citations

Journal ArticleDOI
O. G. McGee1
TL;DR: In this article, the bending stress singularities that occur in the two opposite, clamped-free corners with obtuse angles of the rhombic plates are considered. And the strength of these singularities increases significantly as the obtused angles at the corners increase.
Abstract: In this paper (part I) an ample review of the published literature of skew plate vibrations summarizes well over 100 references as background, bringing forth a need for accurate solutions incorporating stress singularity-based methodologies for analyzing this applied mechanics problem. Such an accurate method is presented in a part II companion paper for analysis of flexural vibrations of rhombic plates with all combinations of clamped and free edge conditions. The prime focus therein is that the analysis explicitly considers the bending stress singularities that occur in the two opposite, clamped-free corners with obtuse angles of the rhombic plates. The strength of these singularities increases significantly as the obtuse angles at the corners increase. Frequency relations summarized herein from this review of Mindlin and Reddy skew plate vibrations research enable investigators to obtain accurate 3–4 significant digit upper bounds on exact solutions of shear deformable skew plates, including the effect...

10 citations

Journal ArticleDOI
O. G. McGee1
TL;DR: In this article, a single-field energy-based Ritz procedure is employed with the dynamical energies derived from classical Kirchhoff thin-plate theory to estimate the normal displacement of a skew rhombic plate.
Abstract: An ample review of the published literature of skew (rhombic) plate vibrations in a companion Part I paper serves as a background that motivates the need for accurate solutions incorporating stress singularity-based methodologies for analyzing the titled problem. Such an accurate method is presented in this Part II paper. The prime focus here is that the vibration analysis explicitly considers the bending stress singularities that occur in the two opposite, clamped-free corners with obtuse angles of the rhombic plates. The strength of these singularities increases significantly, as the obtuse angles at the clamped-free corners exceeds 95o. A single-field energy-based Ritz procedure is employed with the dynamical energies derived from classical Kirchhoff thin-plate theory. The normal displacement of the rhombic plate is approximated as a hybrid series of (i) admissible and mathematically complete algebraic polynomials, and (ii) corner functions which account for both the kinematic boundary conditions and t...

7 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

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