Time Period Analysis of Orthotropic Skew Plate with 2-D Circular Thickness and 1-D Circular Density

Abstract

In the present study, the time period of vibration of an orthotropic parallelogram plate with $2-$ D (two-dimensional) circular thickness under the effect of $2-$ D parabolic temperature is investigated for the first time. The different edge conditions are $CCCC$ , $CCCF$ , $CFCF$ , $CSCF$ , and $SFSF$ boundary conditions, where C, S, and F stands for clamped, simply supported, and free edges of the plate, respectively. The variation in density of plate material is considered to be $1-$ D (one-dimensional) circular. The Rayleigh–Ritz technique is used to solve the differential equation and evaluate the time period for the first two modes of vibration. A convergence study of an orthotropic parallelogram, rectangle plate, and square plate for modes of frequency at various edge conditions is also carried out. The authors performed a comparative analysis of the time period and modes of frequency of orthotropic parallelogram, rectangle plate, and isotropic square plate with the available published results at various edge conditions. The main conclusion which we made from this study is that by choosing the above-mentioned plate parameters, we obtained fewer modes of frequency in comparison to other variations mentioned in the literature. Also, the study suggests that the variation in modes of frequency is less in comparison to other variations.