Element-Free Galerkin Method for Analyzing Size-Dependent Thermally Induced Free Vibration Characteristics of Functionally Graded Magneto-Electro-Elastic Doubly Curved Microscale Shells

Within the framework of consistent couple stress theory (CCST) and employing Hamilton’s principle, we derive a Galerkin weak formulation to analyze the three-dimensional (3D) size-dependent free vibration characteristics of a simply supported, functionally graded (FG) magneto-electro-elastic (MEE) doubly curved (DC) microscale shell subjected to a uniform temperature change. Incorporating the differential reproducing kernel (DRK) interpolants into the weak formulation, we further develop an element-free Galerkin (EFG) method. The microscale shell of interest is composed of two-phase MEE materials, and its material properties are assumed to vary through its thickness according to a power-law distribution of the volume fractions of the constituents. The results show that the natural frequency solutions obtained using the EFG method are in excellent agreement with the reported 3D solutions for laminated composite and FG-MEE macroscale plates, with the material length-scale parameter and the inverse of the curvature radii set to zero. The effects of the material length-scale parameter, temperature change, inhomogeneity index, and mid-surface radius and length-to-thickness ratios on the FG-MEE microscale shell’s free vibration characteristics in a thermal environment are examined and appear to be significant.