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Magnetostrictively induced vibration of film-substrate plates

Abstract:

We present a method to pbkp_redict the dynamic behavior of a magnetostrictive bimorph during free vibration as well as magnetically induced forced vibration. The cases considered are those in which the film and the substrate are mechanically and magnetically isotropic, the magnetization is confined to the plane of the film, and an alternating magnetic field is applied in a direction parallel to the plane of the plate. The calculation scheme proposed is based on a set of nonlinear constitutive laws used to calculate the strains observed in a magnetostrictive material in terms of the stress and the magnetic field applied. The constitutive laws are combined with the classical laminated plate theory to formulate the equations of motion of a magnetostrictive bimorph. In contrast with the expressions derived by previous authors, we consider the magnetic field as one of the independent variables. This feature allows us to calculate not only the natural frequencies of a bimorph but also the frequencies at which a specific magnetic field can be applied to induce resonance in a specimen. To illustrate and validate the method proposed, we consider a cantilever plate and a plate in which all four edges are free. The computations show that the dynamic deformation induced by an in-plane field can include twisting as well as bending deflections. We also show that the direction of application of a magnetic field can be used to tailor the dynamic response of a bimorph. Our calculations are seen to offer significant improvements over the ones obtained with previous models. One of the advantages of the method proposed is that it can be used regardless of the relative thickness of the substrate with respect to that of the film. © 2004 Elsevier B.V. All rights reserved.