Vibrational Study of Square Plate with Thermal Effect and Circular Variation in Density

The paper deals with the study of vibration on the non-homogeneous square plate under temperature environment. It is considered that plate has bi-parabolic temperature variation along the axes. The plate's thickness is to be considered as exponentially along x-axis. All the available literature has been dealt with the assumption that the density varies either linearly or parabolically, but none of them considered other situation. In this paper, the author considered that plate's density varies circular along x-axis. In this study, Rayleigh Ritz technique is applied to obtain the vibrational frequency under different combination of parameters which are involved either in the geometry or property of the material. High-level computational software MAPLE does all the calculations. The results are represented with the help of tables, and a graphical comparison is also made for current study with the existing result in the literature for the support of our study.