Free Vibration of Polar Orthotropic Circular Plates of Variable Thickness With Elastically Restrained Edge

Gupta, Utkarsh; Ansari, A.H.

doi:10.1006/jsvi.1997.1463

Cited by 24 publications

(6 citation statements)

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“…Other authors using the Rayleigh-Ritz method include Singh [17], Gupta [18] and Taher [19], where in the latter case the accuracy was determined through comparisons with finite element calculations.…”

Section: Existing Solutions For Cylindrical Platesmentioning

confidence: 99%

Damping of flexural vibrations in circular plates with tapered central holes

O'Boy

Krylov

2011

Journal of Sound and Vibration

101

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The paper develops a numerical approach to the calculation of mobilities for a circular plate with a tapered central hole of power-law profile. The exact solution of the corresponding flexural wave equation that exists for m = 2 has been used in the process of the numerical solution of the corresponding boundary problem. Note that this value of m belongs to the power-law range m ≥ 2 associated with zero reflection of quasi-plane waves from a tapered hole in geometrical acoustics approximation. Two cases of added damping in the central hole area have been considered: a thin absorbing layer and a constrained layer. Cross and point mobilities have been calculated for both these cases. The obtained results for point and cross mobilities show a substantial suppression of resonant peaks (up to 17 dB), in comparison with the cases of a plate with an uncovered hole of the same power-law profile and of a reference circular plate of constant thickness covered or uncovered by a thin absorbing layer. Further theoretical and experimental research is needed to examine applications of the obtained numerical results to more practical situations, e.g. to rectangular plates or other structures with arbitrary locations of tapered holes.

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Section: Existing Solutions For Cylindrical Platesmentioning

confidence: 99%

Damping of flexural vibrations in circular plates with tapered central holes

O'Boy

Krylov

2011

Journal of Sound and Vibration

101

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“…Laura et al [1}3], and Gupta et al [4,5] investigated the linear free vibrations and buckling of polar orthotropic circular and annular plates using analytical and/or numerical methods. Zheng and Zhou [6], and Zhou et al [7] studied the characteristics of de#ection and free vibration in the vicinity of the de#ection con"guration to the circular plates with geometrically non-linear deformation by means of the semianalytic method.…”

Section: Introductionmentioning

confidence: 99%

Shooting Method for Non-Linear Vibration and Thermal Buckling of Heated Orthotropic Circular Plates

Zhou

2001

Journal of Sound and Vibration

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“…The choice of functions approximating the de#ection function in equation (5) is based upon the static de#ection of polar orthotropic circular plates [1, p. 372], which has faster rate of convergence [7] as compared to polynomial co-ordinate functions [15}19]. The functional J(w) given by (4) on introduction of non-dimensional variables and using relation (5) FORCED AXI-SYMMETRIC RESPONSE OF POLAR ORTHOTROPIC PLATES becomes…”

Section: Energy Expressionmentioning

confidence: 99%