An analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem

Abstract

Based on the Timoshenko beam theory and on the assumption that the electric and magnetic fields can be treated as steady, since elastic waves propagate very slowly with respect to electromagnetic ones, a general analytical solution for the transient analysis of a magneto-electro-elastic bimorph beam is obtained. General magneto-electric boundary conditions can be applied on the top and bottom surfaces of the beam, allowing us to study the response of the bilayer structure to electromagnetic stimuli. The model reveals that the magneto-electric loads enter the solution as an equivalent external bending moment per unit length and as time-dependent mechanical boundary conditions through the definition of the bending moment. Moreover, the influences of the electro-mechanic, magneto-mechanic and electromagnetic coupling on the stiffness of the bimorph stem from the computation of the beam equivalent stiffness constants. Free and forced vibration analyses of both multiphase and laminated magneto-electro-elastic composite beams are carried out to check the effectiveness and reliability of the proposed analytic solution.

Fast multipole boundary element analysis for 2D problems of magneto-electro-elastic media

“…Chen et al [7] obtained a concise general solution for transversely isotropic MEE media involving thermal effect and derived an exact solution of a penny-shaped crack in an infinite body. Milazzo et al [8] studied the forced vibration of a MEE 2 bimorph beam based on the Timoshenko's beam theory.…”

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

“…Milazzo et al [24] analyzed the forced vibrations of MME beams. Ke and Wang [25] used nonlocal theory to study the free vibrations of MEE beam.…”

An Inhomogeneous Cell‐Based Smoothed Finite Element Method for Free Vibration Calculation of Functionally Graded Magnetoelectroelastic Structures

“…Several computational techniques were proposed to investigate the electroelastic, magnetoelastic, and electromagnetic coupling effects of smart structures, such as finite element method (FEM), mesh-free method, and scaled boundary FEM [5][6][7][8][9][10]. Bhangale and Ganesan analyzed the static behaviors of linear anisotropic FGMEE plates using semianalytical FEM and investigated the free vibration of FGMEE plates and cylindrical shells [11,12].…”