<p>On Frequencies of Non-Uniform Rhombic Plate to Mitigate Unwanted Vibration</p>

This study presents a comprehensive analysis of the vibration behavior of a rhombic tapered plate exposed to a two-dimensional temperature distribution. The plate’s thickness is modeled with a bilinear variation, while material non-homogeneity is introduced through an exponential variation of density along the x-direction. Employing the Rayleigh-Ritz method, the governing differential equation is formulated using classical plate theory and solved to obtain the natural frequencies corresponding to the first two modes of vibration. A detailed parametric study is conducted by varying key structural and thermal parameters, including the non-homogeneity index, thermal gradient, aspect ratio, and taper constant. The analysis is carried out for two distinct boundary conditions: fully clamped (C-C-C-C) and fully simply supported (SS-SS-SS-SS). However, the present analysis is limited to linear viscoelastic behavior, small deflection assumptions, and idealized boundary conditions. The results, presented in tabular form, highlight the significant influence of both thermal and geometric factors on the vibrational response of the structure. The study offers valuable insights into the influence of the thermal gradient and structural parameters on the vibration behavior of plate structures.