This study determines the time period of vibrational modes for a non-uniform orthotropic parallelogram plate, featuring a one-dimensional circular thickness variation and subjected to clamped (CCCC) edges. The authors make assumptions about the material; they assume a one-dimensional circular density variation and incorporate Poisson’s ratio to address material non-uniformity. The motivation to choose circular variation in the plate parameter was due to its numerous applications in engineering and real-life applications like engine covers, rotor blades, etc. The authors also account for a parabolic temperature gradient across the plate. Utilizing the Rayleigh–Ritz technique, they derive the frequency equation and solve it to determine the vibration mode time periods. This study includes a convergence analysis of the plate across (CCCC) edge conditions. The primary aim is to demonstrate the advantage of selecting a variable (circular) density and Poisson’s ratio simultaneously over solely varying the density parameter. The secondary aim is to show that the variable Poisson’s ratio is a much better choice in comparison to variable density as a non-homogeneity parameter.