Dynamic behavior of a Micro/Nano-beam made of smart piezoelectric material with property gradient

Abstract

This thesis investigates the static bending and free vibration of functionally graded magneto-electro-elastic (FG-MEE) microbeams in sandwich, coated, and bi-coated forms. Refined higher-order and quasi-3D beam theories are combined with the Differential Quadrature Finite Element Method (DQ-FEM) to capture electromechanical coupling. Material gradation is modeled by a power-law distribution, ensuring smooth property transitions between MEE and non-MEE layers. The Modified Couple Stress Theory (MCST) is incorporated to account for size-dependent effects, and governing equations are derived via Lagrange’s theorem and Gauss–Lobatto discretization. Validation with published results confirms the model’s accuracy and efficiency. Results show that material composition, gradation index, and geometry strongly affect static and dynamic responses. Increasing BaTiO3 enhances piezoelectric deflection, while CoFe2O4 strengthens magnetostrictive effects. Higher gradation indices and slenderness ratios increase stiffness but reduce electromechanical potentials. Natural frequencies are highly sensitive to boundary conditions. The framework offers an efficient tool for optimizing FG-MEE microbeams in smart microsystems.