Vibration of Clamped Visco‐Elastic Rectangular Plate with Parabolic Thickness Variations

Abstract

Most of the machines and engineering structures experience vibration and their design generally requires consideration for their dynamic behavior. Due to this, the study of vibration, as it deals with the vibratory behavior of bodies, is acquiring increasingly importance in several engineering applications, nuclear reactor technology and aeronautical field etc. Most of the work has been done in the field of elastic and non-elastic behavior of the bodies but a very little work is done in the field of visco-elastic bodies with varying thickness. The analysis presented here is to study the effect of taper constants on free vibration of a clamped visco-elastic rectangular plate with parabolically varying thickness. The two-dimensional thickness variation is taken as the Cartesian product of parabolic variations along the two concurrent edges of the plate. Using Rayleigh-Ritz method, frequency equation derives. Logarithmic decrement, time period and deflection for the first two modes of vibration are calculated for various values of taper constants and aspect ratio.

Thermal Effect on Vibration of Tapered Rectangular Plate

“…It is assumed that thickness of the rectangular plate varies parabolically in both directions [11]; that is,…”

“…Gupta and Khanna [10] analyzed time period and deflection for the first two modes of vibrations of viscoelastic rectangular plate with linear thickness variations in both directions. Gupta and Khanna [11] had evaluated time period and deflection for the first two modes of vibration of viscoelastic rectangular plate for biparabolic thickness variation. Lal et al [12] analyzed the transverse vibrations of nonhomogeneous rectangular plates of uniform thickness using boundary characteristic orthogonal polynomials.…”

Thermal Effect on Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variation in Both Directions

“…The aim of present investigation is to study the effect of thermal gradient on the vibration of a clamped visco-elastic rectangular plate whose thickness varies parabolically in both directions, which is an extension of authors' work [7]. Here authors introduced the effect of thermal gradient on their work [7].…”

“…Gupta and Khanna [8] solved the problem of vibration of visco-elastic rectangular plate with linearly thickness variations in both directions. Recently, Gupta and Khanna [7] analyzed the vibration of clamped visco-elastic rectangular plate with parabolic thickness variations. Singh and Chakarverty [17] solved the problem for vibration of skew plates using characteristic orthogonal polynomials.…”

“…Here authors introduced the effect of thermal gradient on their work [7]. It is assumed that the plate is clamped on all the four edges and its temperature varies linearly.…”