Natural Frequencies of Orthotropic, Elliptical and Circular Plates

Kim, C.S.

doi:10.1006/jsvi.2002.5278

Cited by 15 publications

(7 citation statements)

References 24 publications

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“…Because of the symmetry of both the loading and the geometry of the plate, four copies of the first quadrant (the positive x-y plane) may be used when computing the energy of the plate [10]. Hence, substituting the nondimensional variables into Eqs.…”

Section: Fig 2 Location Of the Point Supportsmentioning

confidence: 99%

Static analysis of point-supported super-elliptical plates

Altekin

Altay

2007

Arch Appl Mech

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This paper reports the static analysis of point-supported super-elliptical plates of uniform thickness subjected to a uniformly distributed lateral load. The plate perimeter was defined by a super-elliptic function with a power, corresponding to shapes ranging from an ellipse to a rectangle. The analysis was based on the Kirchhoff-Love plate theory and the computations were carried out by the Ritz method. Lagrange multipliers were used to satisfy the boundary conditions. Isotropic and homogeneous plates with 20 different shapes were examined for two distinct aspect ratios. Convergence studies were performed for the central deflection and the central bending moments. The results were checked against those of a corner-supported square plate and good agreement was obtained.

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Section: Fig 2 Location Of the Point Supportsmentioning

confidence: 99%

Static analysis of point-supported super-elliptical plates

Altekin

Altay

2007

Arch Appl Mech

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“…Hassan and Markary (2003) utilized the Rayleigh–Ritz method to study transverse vibration of elliptic plates of linearly varying thickness with half of the boundary clamped and the rest simply supported. Kim (2003) studied natural frequencies of orthotropic elliptic and circular plates using simple polynomials in the Rayleigh–Ritz method. Numerical solutions for frequencies and mode shapes for elliptical plates of uniform/variable thickness with mixed boundary conditions have been obtained by Hassan (2004a, 2004b) using the Rayleigh–Ritz method.…”

Section: Platesmentioning

confidence: 99%

The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review

Kumar¹

2017

Journal of Vibration and Control

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The Rayleigh–Ritz method is a classical method that has been widely used to investigate dynamic, static and buckling behavior, i.e., the natural frequencies, mode shapes, moments, stresses, critical buckling loads of vibrating structures and to solve boundary value problems. Different developments in the method have taken place from time to time. This paper presents a comprehensive literature review on the application of the Rayleigh–Ritz method to analyze vibration, static and buckling characteristics of beams, shells and plates using different theories.

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“…On the other hand, the free-vibration analysis of orthotropic generally shaped plates has been much less addressed. Specifically, few common cases have been studied in the literature, such as elliptical or circular plates [17], general triangular plates [18], skew plates [19], and trapezoidal plates [20].…”

Section: Introductionmentioning

confidence: 99%