Exploring porosity impact on the free vibration of FG plates using trigonometric shear deformation theory

This study investigates the free vibration behavior of functionally graded (FG) plates using trigonometric shear deformation plate theory. The novelty of this work lies in the incorporation of porosities, which are inherent in FG materials due to manufacturing processes, and their detailed impact on the vibrational performance of these plates. Unlike existing studies, this research comprehensively examines multiple porosity distribution patterns, including homogeneous, "O", "X", and "V" configurations, which are seldom analyzed together. The governing equations of motion are derived using Hamilton's principle and solved analytically with the Navier method for simply supported boundary conditions. A key contribution of this study is the exploration of how porosity levels, distribution types, and geometry parameters collectively influence the natural frequencies of FG plates. The results highlight the significant effect of different porosity patterns, with "X"-shaped porosity yielding the highest natural frequency and homogeneous distribution leading to the lowest. Furthermore, the findings reveal that increased porosity levels can either enhance or diminish the vibrational characteristics depending on the distribution pattern. These insights provide valuable guidance for optimizing the design of FG plates for various engineering applications, such as aerospace and biomedical industries.