Free vibration analysis for homogenous magneto-electro-elastic plates using the moving Kriging meshfree method

Abstract

This paper presents the free vibration analysis of homogeneous magneto-electro-elastic (MEE) plates using a refined first-order shear deformation theory (RFSDT) and the moving Kriging meshfree method. The RFSDT, which includes only four variables, one less than the classical first-order shear deformation theory, streamlines the analysis. The MEE materials, which exhibit coupled piezoelectric and piezomagnetic effects, are composed of BaTi2O3 and CoFe2O4. The magnetic and electric potentials, which satisfy Maxwell's equations, are assumed to vary along the plate thickness in a combination of cosine and linear patterns. The coupled governing equations of motion for the MEE plates are derived using the principle of extended virtual displacement. These equations are then solved to determine the natural frequencies of the MEE plates using the moving Kriging meshfree method. Several numerical examples are analyzed to assess the impact of geometrical parameters on the natural frequencies of the MEE plates.

Keywords: Magneto-electric-elastic functionally graded plates; moving Kriging meshfree method; free vibration; refined firstorder shear deformation theory.