This paper demonstrates the wide – ranging contrast of analytical and numerical approaches to scrutinize the trapezoidal – shaped plates vibrational – pattern under the mixed edge restrictions, subjected to bi – exponentially alteration of thickness and heat flow gradient. These trapezoidal – shaped plates are often employed in numerous fields including space-technology, machinery domain, infrastructure and constructions, ocean engineering, heat transfer domain and energy system domain etc. The major intension of this paper is to observe how numerous alterations in edge restrictions and modelling strategy affects the predicted modal – frequencies and vibrational – patterns of the plates. We employ the Rayleigh – Ritz strategy to calculate the system of equations. At the end of this paper, I have compare my outcomes with those of existing study by scrutinizing the factors such as: frequency – pattern and non – uniformity constant and summarizing the evaluation in table for accuracy. The computational – based software “Maple” in order to employed model – frequency values to ensure the precision and efficiency in my analysis.