Closed Form Expression for the Vibration Problem of a Transversely Isotropic Magneto-Electro-Elastic Plate

Abstract

A closed form expression for the transverse vibration of a magnetoelectroelastic (MEE) thin plate is derived, and the exact solution for the free vibration of a two-layered BaTiO3–CoFe2O4 composite is obtained. Based on the Kirchhoff thin plate theory, the bending problem of a transversely isotropic MEE rectangular plate is investigated, and the governing equation in terms of the transverse displacement is then presented in a rather compact form. The material coefficients for such MEE plate are expressed uniquely by the volume fraction (vf) of the two-layered BaTiO3–CoFe2O4 composite, which indicates a transversely isotropic MEE medium. The natural frequencies of such MEE plate are evaluated analytically, and the effects of different volume fractions on the natural frequency are further discussed.

Variable kinematics models and finite elements for nonlinear analysis of multilayered smart plates

“…Actually, the variational statement given by Eq. (10) represents the extension of the Principle of Virtual Displacements (PVD) to MEE structures for a total lagrangian formulation. From Eq.…”

“…An alternative modeling strategy consists in condensing the magneto-electric state into the plate kinematics, invoking quite general a priori assumptions on its behaviour; actually this reduces the smart plate model to that of an effective mechanical plate. This approach has proven effective for thin homogeneous MEE plates [10,11] and for thin to moderately thick laminated plates [12,13]. More recently, the author proposed the application of this approach to systematically build families of smart plate models [14,15] through the technique known as Carrera Unified Formulation (CUF) [16].…”

Free vibration analysis of magneto-electro-elastic microbeams subjected to magneto-electric loads

“…Liu and Chang [14] presented a closed form solution for the vibration problem of a transversely isotropic MEE plate. Pan [13] presented an exact closed-form solution for the static deformation of a layered MEE plate based on a new and simple formalism resembling the Stroh formalism.…”

Vibration Analysis of a Magnetoelectroelastic Rectangular Plate Based on a Higher-Order Shear Deformation Theory

“…Ramirez et al (2006b) also determined natural frequencies of orthotropic magnetoelectroelastic graded composite plates by using a discrete layer model. Liu and Chang (2010) derived a closed form expression for the transverse vibration of a magnetoelectroelastic thin plate and obtained the exact solution for the free vibration of a twolayered BaTiO 3 -CoFe 2 O 4 composite. Single-layer approaches to static and free vibration analysis of magnetoelectroelastic laminated plates have also been introduced (Milazzo 2012(Milazzo , 2014a(Milazzo , 2014bMilazzo and Orlando, 2012).…”