Application of Hashin–Shtrikman bounds homogenization model for frequency analysis of imperfect FG bio-composite plates

Despite abundant theoretical investigations on the dynamic behavior of functionally graded (FG) structures, the study on frequency analysis of FG bio-composite structures is limited. FG bio-composite materials due to their biocompatibility potentials and good material properties can be applied in biomedical applications, especially dental implants. In this investigation, a natural frequency response of the FG bio-composite plate is analyzed within the framework of the newly developed refined higher-order shear deformation plate theory. Additionally, the imperfection impact on frequency behavior is evaluated while three imperfection distribution patterns are taken into account. The constitutive materials of FG bio-composite plate are Hydroxyapatite and Titanium. The effective material properties of the structure are determined with the help of the upper Hashin–Shtrikman bounds homogenization model. In continuation, to solve the derived governing equations of imperfect FG bio-composite plate, Galerkin's analytical method is employed. Also, the precision of the used theory is validated, the obtained outcomes are compared and an acceptable matching is found. Later, the sensitivity of different considerable variables is comprehensively assessed and discussed.