Vibration frequencies of a rectangular plate with linear variation in thickness and circular variation in Poisson’s ratio

Abstract

The frequency for the first two modes of vibration of a nonhomogeneous tapered rectangular plate is calculated under a bi linear (i.e., linear along both the axes) temperature field. For consideration of the nonhomogeneous material, the author assumed circular variation in Poisson's ratio. Tapering in the plate is assumed to be linear in one direction. The results are calculated for different values of plate parameters and presented with the help of graphs. Comparison of the results is also given, to support the results of the present study.

Vibrational analysis of orthotropic rectangular plate having combination of circular thickness and parabolic temperature

“…In [4], a new analytical solution utilizing a double finite sine integral transform technique was introduced for the vibration response of plates reinforced by orthogonal beams. In [5], the Rayleigh Ritz method was utilized to determine the frequency of an orthotropic rectangular plate, whereas in [6], the time period of transverse vibration of a skew plate with different edge conditions was assessed. In [7], the influence of temperature on the frequencies of a tapered plate was discussed, while [8] investigated a non-uniform triangular plate subjected to a two-dimensional parabolic temperature distribution.…”

Behavior of frequencies of orthotropic rectangular plate with circular variations in thickness and density

“…Free vibration analysis of isotropic and laminated composite plate [10] on elastic point supports using finite element method (FEM) is studied. Vibration frequencies of a rectangular plate with linear variation in thickness and circular variation in Poisson's ratio was provided in [11]. Thermally induced vibrations of shallow functionally graded material arches is considered and analyzed in [12] by using classical theory of curved beams.…”

Temperature effect on frequencies of a tapered triangular plate

“…One-dimensional thermal and two dimensional thickness effect on frequency of traingle plate [16] has been computed on clamped edge conditons. Vibrational freuquency of rectangle plate [17,18] comprises the nonhomogeneity, and the Poisson's ratio effect has been investigated under the temperature field. The Rayleigh-Ritz technique has been employed to investigate the frequency modes of a skew plate [19,20] made of nonhomogeneous material with temperature effect.…”