Active control of beam with magnetostrictive layer

Layerwise partial mixed finite element analysis of magneto-electro-elastic plates

Abstract: In this paper a partial mixed layerwise finite element model for adaptive plate structures is presented. Static analysis of magneto-electro-elastic laminated plate structures is considered. The mixed finite element formulation is obtained by considering a Reissner mixed variational principle. The mixed functional is formulated using transverse stresses, displacement components and electric and magnetic potentials as primary variables. The other fields are calculated by post-computation through constitutive equations. The numerical results obtained by the present model are in good agreement with available three-dimensional analytical solutions.

Vibration suppression of laminated composite beams using actuators of giant magnetostrictive materials

Abstract: This paper presents a simulation of vibration suppression of a laminated composite beam embedded with actuators of a giant magnetostrictive material subjected to control magnetic fields. It has been found that the strains generated in the material are not only significantly larger than ones created by many other smart materials but also exhibit some inherent nonlinearities. To utilize the full potential of these materials in active vibration control, these nonlinearities should be characterized in the control system as accurately as possible. In this simulation of nonlinear dynamic controls, the control law with negative velocity feedback and the analytical nonlinear constitutive model of the magnetostrictive layer are employed. The numerical results show that this proposed approach is efficient not only in a linear zone but also in nonlinear zones (dead zone and saturation zone) of magnetostrictive curves in vibration suppression. Compared with those from the control system based on the linear constitutive relations of the material, it is found that the simulation results based on the linear model are efficient only when the magnetostrictive relations are located in the linear zone. Once the system has some departure from the linear zone, however, the results from the linear model become unacceptable. Finally, the effect of material properties, lamination schemes and location of the magnetostrictive layers on vibration suppression of the practical system is evaluated.

Vibration suppression of cantilever laminated composite plate with nonlinear giant magnetostrictive material layers

Abstract: In this paper, a nonlinear and coupled constitutive model for giant magnetostrictive materials (GMM) is employed to predict the active vibration suppression process of cantilever laminated composite plate with GMM layers. The nonlinear and coupled constitutive model has great advantages in demonstrating the inherent and complicated nonlinearities of GMM in response to applied magnetic field under variable bias conditions (pre-stress and bias magnetic field). The Hamilton principle is used to derive the nonlinear and coupled governing differential equation for a cantilever laminated composite plate with GMM layers. The derived equation is handled by the finite element method (FEM) in space domain, and solved with Newmark method and an iteration process in time domain. The numerical simulation results indicate that the proposed active control system by embedding GMM layers in cantilever laminated composite plate can efficiently suppress vibrations under variable bias conditions. The effects of embedded placement of GMM layers and control gain on vibration suppression are discussed respectively in detail.

A regular variational boundary model for free vibrations of magneto-electro-elastic structures

Abstract: In this paper a regular variational boundary element formulation for dynamic analysis of two-dimensional magneto-electro-elastic domains is presented. The method is based on a hybrid variational principle expressed in terms of generalized magneto-electro-elastic variables. The domain variables are approximated by using a superposition of weighted regular fundamental solutions of the static magneto-electro-elastic problem, whereas the boundary variables are expressed in terms of nodal values. The variational principle coupled with the proposed discretization scheme leads to the calculation of frequency-independent and symmetric generalized stiffness and mass matrices. The generalized stiffness matrix is computed in terms of boundary integrals of regular kernels only. On the other hand, to achieve meaningful computational advantages, the domain integral defining the generalized mass matrix is reduced to the boundary through the use of the dual reciprocity method, although this implies the loss of symmetry. A purely boundary model is then obtained for the computation of the structural operators. The model can be directly used into standard assembly procedures for the analysis of non-homogeneous and layered structures. Additionally, the proposed approach presents some features that place it in the framework of the weak form meshless methods. Indeed, only a set of scattered points is actually needed for the variable interpolation, while a global background boundary mesh is only used for the integration of the influence coefficients. The results obtained show good agreement with those available in the literature proving the effectiveness of the proposed approach.

Optimization and Dynamic Modeling of Galfenol Unimorphs

Abstract: Design and modeling of a bi-laminate, Galfenol-driven composite beam is presented in which the elasticity of the adhesive layer is considered. The optimal thickness ratio necessary to maximize the tip deflection is found by minimization of the internal energy of the beam. Model simulations show that use of a substrate material with high modulus leads to larger tip deflections. Stainless steel was therefore utilized as substrate in the experiments. In order to reduce eddy currents, a laminated silicon steel frame was employed to magnetize the beam. A dynamic model is proposed by coupling the structural dynamics of the beam and adhesive layer with the magnetostriction generated by the Galfenol layer. The latter is described with a linear piezomagnetic law with uniform magnetic field distribution along the length of the beam. Galerkin discretization combined with Newmark numerical integration are employed to approximate the dynamic response of the beam. The model is shown to describe both the transient and s...

Structural magnetic strain model for magnetostrictive transducers

Abstract: This paper addresses the modeling of strains generated by magnetostrictive transducers in response to applied magnetic fields. The measured strains depend on both the rotation of moments within the material in response to the field and the elastic properties of the material. The magnetic behavior is characterized by considering the Jiles-Atherton mean field theory for ferromagnetic hysteresis in combination with a quadratic moment rotation model for magnetostriction. Elastic properties must be incorporated to account for the dynamics of the material as it vibrates. This is modeled by force balancing, which yields a wave equation with magnetostrictive inputs. The validity of the resulting transducer model is illustrated by comparison with experimental data.

The use of magnetostrictive particle actuators for vibration attenuation of flexible beams

Abstract: A laminated composite beam, representative of a flexible beam, containing a layer of magnetostrictive material, is considered as a distributed parameter system and its dynamic behavior has been investigated. The magnetostrictive layer is used to induce actuation forces to control vibration in the beam, following a velocity feedback control law. The dynamic behavior of the beam is studied to illustrate the effect of the lay!up sequence, the weight of the coil, the control gain and the concentrated mass on the vibration suppression capability. Numerical results have been given for three different lay- up sequences of the laminates, representing a wide range of stiffness variation. The controllability of the first four modes, the corresponding coil current and the stresses have also been discussed. The results clearly indicate viability of developing a smart flexible beam with embedded magnetostrictive particle layers.