Analytical Solution for Free Vibration of Laminated Curved Beam with Magnetostrictive Layers

Abstract

An analytical model to study the free vibration suppression of laminated curved beam with embedded actuating layers is presented in this study. The magnetostrictive layers are used to control and enhance the vibration suppression. The governing differential equations of the model are derived using the Hamilton principle. Analytical solution of the equations governing laminated curved beam with embedded magnetostrictive layers are obtained for simply-supported boundary conditions. Velocity feedback with constant gain distributed controller, by using Terfenol-D as smart material, is chosen to achieve vibration suppression. The effects of material properties, radius of curvature, lamination scheme, and placement of magnetostrictive layers with respect to laminate midplane on vibration suppression are studied in details.