Effect of linear thermal gradient on vibrations of trapezoidal plates whose thickness varies parabolically

Abstract

Plates of variable thickness are widely used in modern technology nowadays in various engineering fields, such as marine engineering, aeronautical fields, nuclear reactors etc. The present paper is a study of linear thermal gradient on the vibration of trapezoidal plates with parabolically varying thickness. The Rayleigh Ritz technique is used to get the required frequency equation. In the present investigation, the effect of various factors, i.e. thermal gradient, taper constant and aspect ratio are studied to calculate the frequencies corresponding to the first two modes of vibration and are presented in tabular and graphical form.

Study of Thermally Induced Vibration of Non-Homogeneous Trapezoidal Plate with Varying Thickness and Density

“…The frequencies for the first two modes of vibration are obtained for C-S-C-S non-ho mogeneous trapezoidal plate by Rayleigh-Rit z method. The authenticity and accuracy of numerical results of the present work has been verified with the authors published paper [25]. Results are presented in tabular form.…”

“…The accuracy of the present computations is compared with the published results [25] for C-S-C-S non-homogeneo us trapezoidal plate with non-homogeneity constant 1 α = 1.0, aspect ratio a/b = 1.0, c/b = 0.5, 1.0 and thermal gradient β = 0.0 to 1.0 and taper constant α = 0.0 to 1.0. Table 1 , 2, 3 and 4 shows a co mparison of the values of frequency parameter obtained in the present problem and published paper of the authors [25]. A very close agreement is seen between the present results and of the published paper in which ho mogeneous plate with parabolically varying thickness (density is constant) has been considered.…”

Vibration of woven fiber laminated composite plates in hygrothermal environment

“…Fakhari and Ohadi (2011) studied the large amplitude vibration of functional graded material (FGM) plates under thermal gradient and transverse mechanical loads using the FEM. Gupta and Sharma (2011) investigated the effect of linear thermal gradient on vibrations of trapezoidal plates whose thickness varies parabolically using the Raleigh Ritz Technique.…”

Study of Thermally Induced Vibration of Non-Homogeneous Trapezoidal Plate with Parabolically Thickness Variation in Both Directions

“…Gupta and Sharma [22] studied the effect of thermal gradient on transverse vibration of non-homogeneous orthotropic trapezoidal plate of parabolically varying thickness. Gupta and Sharma [23] observed the effect of linear thermal gradient on vibrations of trapezoidal plates whose thickness varies parabolically. Gupta and Sharma [24] study the thermally induced vibration of non-homogeneous trapezoidal plate with varying thickness and density.…”