The Mechanics of Magnetoelectroelastic Laminates

Abstract

The through-thickness fields of laminates composed of elastic, piezoelectric, and magnetostrictive layers are considered under static and dynamic conditions to determine their fundamental behavior and investigate the limits of simplified plate theories in which the fields are assumed to possess a specific type of behavior. The weak form of the equations of motion/equilibrium, Gauss’s law in the absence of charge density, and Gauss’s law for magnetism are formulated for a rectangular laminate with arbitrary edge boundary conditions under the application of applied surface displacement/traction, scalar potential/electric flux, or vector potential/magnetic flux. The layers within the laminate are allowed to possess any linear constitutive law consistent with a magnetoelectroelastic solid, and the number of layers is arbitrary. Using the Ritz method, approximate solutions to the displacements, electrostatic potential, and vector potential are sought to the weak form of the governing equations. Using linear combinations of through-thickness approximations along with separate approximations for the in-plane behavior allows an accurate representation of the break in variable slope across an interface with dissimilar material properties. The model is applied to problems with known exact solutions (static load with simple support and free vibration with simple support), and excellent agreement is obtained.