Bending and Vibration Analysis of Magneto-Electro Bilaterally Coated Quasi-3D Microbeam Via DQ-FEM

Abstract In this study, the static bending and free vibration of a bilaterally coated magneto electro elastic (MEE) functionally graded (FG) microbeam is analysed by using a high order quasi-3D beam theory, along with a Differential Quadrature Finite Element Method (DQ-FEM). The power formulation for FG gradation through the thickness direction is considered. The microbeam consists of two materials, one possessing piezo-magneto-electric characteristics and the other without them. The material characteristics are progressively graded from the outermost surfaces to the innermost core. In order to localize the microstructural effect of the beam, the modified couple stress theory (MCST) is incorporated. By the application of Lagrange's theorem and Gauss-Lobato node scheme, the general governing equation are established. Through the implementation of the established model, “the static bending and free vibration” analysis are determined. To illustrate the effectiveness and accuracy of this particular numerical resolution method, the obtained results are validated with similar outcomes in existing literature. The effects of the material gradation volume fraction index, and the length-thickness ratio on the natural frequencies and static bending are investigated. The results reveal that the material distribution plays a significant role in influencing both static bending and free vibration behavior. Material composition plays a critical role, with higher proportions of MEE material enhancing the piezoelectric effect and magnetostrictive response, respecting the material gradation with optimized combinations of MEE material for higher deflection and optimal electric and magnetic potentials. This study provides a comprehensive framework for optimizing MEE microbeams in applications requiring precise control of mechanical, electrical, and magnetic responses.