Time Period of Thermal-Induced Vibration of Skew Plate with Two-Dimensional Circular Thickness

Abstract

In this study, two-dimensional circular thickness effects on time period of skew plate made with nonhomogeneous material properties are computed in variable temperature environment. Clamped $\left(C\right)$ , simply supported $\left(S\right)$ , and free-edge $\left(F\right)$ conditions are the various combinations considered in this work. One-dimensional circular density and two-dimensional parabolic temperature variation on the plate are considered due to the nonhomogeneous nature of the material and variable temperature environment. Rayleigh–Ritz method is used to compute the time period for the first two modes of vibration. A convergence study of frequency modes of skew plate on various edge conditions has also been performed. The present work has been compared with the frequency modes of parallelogram and rectangle plate on various edge conditions. The objective of the study is to present a numerical data of time period as well as to show how one can control the frequencies of plate by taking an appropriate variation in plate parameters.