Dynamic response of imperfect functionally graded plates: Impact of graded patterns and viscoelastic foundation

This study presents a methodical investigation into improving structural designs through the analytical examination of the dynamic behavior of functionally graded plates (FGPs) resting on viscoelastic foundations. By employing a four variable first- order shear deformation theory, the study computes non- dimensional frequencies for a variety of porous FGPs with diverse graded patterns and porosity distributions. Different gradient patterns of the plates are considered, and three distinct functions- sigmoid (S-FGM),- FGM), exponential (E-FGM),- FGM), and power- law (P-FGM)-are- FGM)-are utilized to assess material performance in specific directions. The equations of motion are derived and solved using both Navier's method and Hamilton's principle. Analytical solutions for vibration frequency are provided to validate the proposed methodology against existing literature. Furthermore, a comprehensive parametric analysis is conducted, taking into account various factors such as ceramic material, porosity distribution, gradient index, length- to- thickness ratio, gradient pattern, and damping coefficient. The findings suggest that enhancing the damping coefficient of the viscoelastic foundation can significantly improve the free- vibrational response of functionally graded material plates.