Two-dimensional dynamic model for composite laminates with embedded magnetostrictive materials

A nonlinear, two-dimensional plate model is presented that describes the dynamic response of composite laminate structures with embedded magnetostrictive materials. The model consists of Navier’s equation coupled with a discrete energy-averaged constitutive model for magnetostrictive materials. Assuming a thin composite geometry, the complete three-dimensional model is reduced to a two-dimensional equivalent single layer plate model by assuming a functional form for displacements. The resulting two-dimensional variational form, solved using finite element software, is applied to analyze the displacements of a Galfenol–aluminum composite actuator, wherein Galfenol sheets are embedded into an aluminum substrate. The model is validated at lower frequencies using time domain measurements of the dynamic actuation response of the actuator. This framework is subsequently utilized to perform a parametric study to maximize the tip displacements by varying the geometric parameters: Galfenol location, thickness ratio, and substrate properties. The general finite element framework presented in this paper is applicable to a wider range of magnetostrictive materials and complex composite geometries.