Efficient and robust nonlinear model for smart materials with application to composite magnetostrictive plates

Abstract

A bidirectionally coupled magnetoelastic model and its validation using a Galfenolunimorph sensor C Mudivarthi, S Datta, J Atulasimha et al. AbstractThis paper investigates the semi-active control of a magnetically-tunable vibration absorber's resonance frequency. The vibration absorber that is considered is a metal-matrix composite containing the magnetostrictive material Galfenol (FeGa). A single degree of freedom model for the nonlinear vibration of the absorber is presented. The model is valid under arbitrary stress and magnetic field, and incorporates the variation in Galfenol's elastic modulus throughout the composite as well as Galfenol's asymmetric tension-compression behavior. Two boundary conditions-cantilevered and clamped-clamped-are imposed on the composite. The frequency response of the absorber to harmonic base excitation is calculated as a function of the operating conditions to determine the composite's capacity for resonance tuning. The results show that nearly uniform controllability of the vibration absorber's resonance frequency is possible below a threshold of the input power amplitude using weak magnetic fields of 0-8 kA m −1 . Parametric studies are presented to characterize the effect on resonance tunability of Galfenol volume fraction and Galfenol location within the composite. The applicability of the results to composites of varying geometry and containing different Galfenol materials is discussed.

Globally convergent nonlinear 3D inverse model for smart materials with Hessian-based optimization

“…Tari et al [29] addressed this shortcoming through a reformulation of this direct model with an exact solution procedure. In addition, Tari et al [30] recently presented an efficient inverse model for a partially coupled magnetomechanical system, in which stresses must be found for given field values. The model was successfully applied to a composite magnetostrictive plate operating in actuation mode.…”

“…Additionally, the inverse model is integrated into a finite-element framework to simulate an aluminum-Galfenol composite plate actuator. Tari et al [30] recently presented a reduced 2D model for this composite plate with the assumption that the magnetic field distribution throughout the Galfenol volume is approximately uniform for the small deformations, thus they assumed that the magnetic field is known. However, we lift this assumption in this work, and simulate this composite plate actuator in full 3D.…”

“…Finally, the remaining unknown derivative terms in eqs. (28)- (30) are obtained from differentiating eq. (24) with respect to field and stress as…”

“…Input alternating and bias magnetic fields of different amplitudes and frequencies (ranging from 0.1 Hz to 250 Hz) were generated using a conductive coil, and the displacement data at the tip of the Galfenol patch (labeled in Figure 2) was collected. Tari et al [30] recently presented a reduced 2D model for this composite plate with the assumption that the magnetic field distribution throughout the Galfenol volume is approximately uniform for the small deformations, thus they assumed that the magnetic field is known. However, we lift this assumption in this work, and simulate this composite actuator in full 3D.…”

“…The governing equations describe structural behavior, electromagnetic behavior, and material constitutive behavior. Following Tari et al [30], the structural behavior is described by the weak form of the 3D Navier's equation as…”