Free asymmetric transverse vibration of polar orthotropic annular sector plate with thickness varying parabolically in radial direction

Abstract

In the present paper, free asymmetric transverse vibrations of a nonuniform polar orthotropic annular sector plate, with parabolically varying thickness in the radial direction, have been studied on the basis of classical plate theory. The circular edges of the plate are elastically restrained against translation and rotation while the straight (radial) edges are simply-supported. Fourth-order linear differential equations with variable coefficients governing the motion have been solved by using the collocation interpolation technique with Chebyshev points as the interpolating nodes. Frequency parameters of the plate with flexible boundary conditions at the circular edges for some typical values of the taper parameters, the rigidity ratios and the radii ratio have been presented.

Geometrically non-linear bending analysis of thick two-directional functionally graded annular sector and rectangular plates with variable thickness resting on non-linear elastic foundation

“…Although a rather large amount of work has been done on tapered beams [87][88][89] and variable thickness circular [9,10,[90][91][92][93][94] and rectangular [95][96][97] plates, but the literature on the variable thickness annular sector plates is scarce. Stability [98], vibration [99][100][101] and bending [102,103] analysis of annular sector plates M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 5 with variable thickness were investigated. According to the review of open literature, geometrically non-linear bending analysis of tapered thickness sectorial plates is not still available, which this void stimulated the authors to study the effect of thickness variation on non-linear bending of sectorial plates.…”

Free Vibration of Annular Circular Plates Based on Higher-Order Shear Deformation Theory: A Spline Approximation Technique

“…Furthermore, isotropic annular circular plates were studied using the exact element method by Efraim and Eisenberger [25], and an annular circular plate attached to a free rigid core was studied by Wang [26]. Moreover, annular circular plates resting on elastic foundation were studied by Celep and Turhan [27], Utku et al [28], and Kukla and Szewczyk [29]; Singh and Jain [30,31] examined the free vibration annular circular plate on elastic edges. Free vibration of annular circular plates resting on Pasternak foundation was studied by Tajeddini et al [32].…”

Free Vibrations of Non-Homogeneous Tapered Square Plate With Bi-Directional Temperature Variations

“…Nagaya [11] discussed the vibrations and dynamic response of visco-elastic plates on non-periodic elastic supports. Singh & Jain [12] studied the free asymmetric transverse vibration of polar orthotropic annular sector plate with thickness varying parabolically in radial direction. Here, Rayleigh Ritz technique is applied to calculate the frequency for the first two modes of vibrations for non-homogeneous tapered clamped square plate with different values of thermal gradient, taper constant and non-homogeneity constant by the help of latest software 'Mathematica'.…”