An analytical solution for vibration analysis of sandwich plates with auxetic core and functionally graded faces in a thermal environment

This study investigates the free vibration characteristics of rectangular sandwich plates that are partially supported by two-parameter elastic foundations, while also accounting for environmental temperature variations. The sandwich plate is constructed with an auxetic core layer, which exhibits a negative Poisson's ratio (NPR), complemented by two functionally graded (FG) face layers. The analysis considers the foundation's capacity to support the plate in either a complete or partial manner. Utilizing Hamilton's principle, the governing equations are derived based on a higher-order shear deformation theory framework. The application of this analytical method to the governing partial differential equations (PDEs) yields a system of algebraic equations. Solving this system in accordance with the specified boundary conditions results in an eigenvalue problem, which facilitates the determination of the natural frequencies of the plate. The findings of this study are validated against existing literature. Furthermore, the investigation explores the impact of various parameters including temperature fluctuations, characteristics of the auxetic core, boundary conditions, elastic foundation distribution patterns, and spring coefficients on the free vibration behavior of the sandwich plate. The results indicate that the auxetic core, characterized by its negative Poisson's ratio, confers metamaterial properties, thereby suggesting that the proposed model possesses significant potential for diverse engineering applications. In this analysis, higher-order shear deformation theory (HSDT) is employed to examine the free vibration characteristics of the sandwich plate, which features an auxetic core and functionally graded faces, while being subjected to a thermal medium and resting on a two-parameter elastic foundation. Given that the material properties of the NPR auxetic core layer are influenced by three geometric parameters, a thorough examination of the effective material properties is conducted, leading to the computation of the natural frequencies of the sandwich plate.