Free Vibration Analysis of Relatively Thick Functionally Graded Plates Under Thermal Environment by Using a Meshfree Method

In this study, the free vibration behavior of functionally graded (FG) plates under a thermal environment is investigated based on a meshfree method and the Reissner-Mindlin plate formulation. FG material (FGM) is a special composite composed of two constituents, ceramic and metal, that possess continuous material properties variation in a certain direction. The material properties of FG plates in this article, in particular, have a power-law distribution through the thickness. Furthermore, temperature is considered a major factor that influences the change in mechanical characteristics of FGM. As a result, it is vital to investigate the mechanical behavior of FG plates in a thermal environment with varying temperature conditions in order to better understand the effect of temperature on this type of material. The Radial Point Interpolation Method (RPIM), which possesses the desired Kronecker delta property, is the meshfree concept used in this paper. And to create the formulation for the rather thick FG plates in the study, the well-known Reissner-Mindlin plate theory is used. The natural frequencies and mode shapes of FG plates subjected to homogeneous temperature change are presented through various numerical examples. The obtained results show that the ambient temperature and the FGM volume fraction index are the parameters affecting the free vibration behavior of the plates. The numerical results of the study are verified with previous publications and show good agreement.