Aerospace Engineering

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Nonlinear and hysteretic magnetomechanical model for magnetostrictive transducers

1999 , Dapino, Marcelo , Alison B. Flatau , Aerospace Engineering

The growing interest on magnetostrictive materials for generation of strains and forces in smart structure systems motivates the development of increasingly accurate models of the performance of these materials as used in transducers. The proposed magnetomechanical model provides a characterization of the material magnetization as well as the strain and force output by a transducer in response to quasistatic applied magnetic fields. The model is built in three steps. In the first, the mean field model for ferromagnetic hysteresis originally developed by Jiles and Atherton is used to compute the magnetization arising from the application of magnetic fields. While this model provides an accurate characterization of the field-induced magnetization at constant stress, it is insufficient in cases where the stress state of the magnetostrictive driver varies significantly during operation. To model the stress-induced magnetization changes, or magnetomechanical effect, a 'law of approach' to the anhysteretic magnetization is considered. The magnetization hysteresis model in combination with this law of approach provides a more realistic representation of the bidirectional energy transduction taking place in magnetostrictive transducers. In the second step, an even-term series expansion posed in terms of the magnetization is employed to calculate the magnetostriction associated with magnetic moment rotations within domains. While the magnetostriction provides a good description of the total material strain at the low field levels where elastic dynamics are of secondary significance, it is highly inaccurate at higher drive levels, in which the elastic response gains significance. This elastic or material response is considered in the third and last step, by means of force balancing in the form of a PDE system with magnetostrictive inputs and boundary conditions consistent with the transducer mechanical design. The solution to this PDE system provides the longitudinal displacements and corresponding strains and forces generated by the magnetostrictive driver. Since the formulation precludes analytic solution, a Galerkin discretization is employed to express the PDE in the form of a temporal system, which is subsequently solved using finite difference approximations. The ability of the model to accurately characterize the magnetomechanical behavior of magnetostrictive transducers is demonstrated via comparison of model simulations with experimental measurements collected from two Terfenol-D transducers.

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Vibrational and acoustic response of ribbed plates

1993 , Juang, Ten-Bin , Anna L. Pate , Alison B. Flatau , Aerospace Engineering

A self-consistent mathematical formulation, using the Fourier transform method and a direct Gaussian numerical integration scheme, is developed and verified for analysis of both vibrational and acoustic responses of infinite submerged ribbed plates. Further steps developed from standard theories make structural intensity, acoustic intensity, and acoustic power calculations possible in the nearfield and farfield, and are demonstrated in this work;The direct numerical integration scheme adopted to obtain responses has proved to be straightforward and reliable. Although the double integration expression in some responses makes the technique infeasible, a practical way to overcome that difficulty is demonstrated using a standard branch-cut integration to eliminate one integration step analytically. The model and numerical scheme readily allow investigation of additional interesting topics, like the passband and stopband characteristic and the mode localization phenomenon that are observed in ribbed structures. Furthermore, an extension to comprehension of the mechanisms that generate the mode localization phenomenon on disordered structures has been realized;A secondary effort examines natural modes of vibration and acoustic radiation for finite stiffened multiple-span beams with the efficient transfer matrix method. This model shows that the mode localization phenomenon exists on disordered stiffened beams both under free-free and hinged-hinged end conditions. The sensitivity of the response to attachment disorder (perturbations in rib stiffness and location) has also been examined. An elaborate vibrational and acoustic experiment has been carried out on a baffled, stiffened, two-span, hinged beam to examine the existence of the localized modes and verify the predicted acoustic responses. Moreover, the radiation efficiency of finite beams has been investigated for comparison of the radiation behavior presented by the different stiffened beam arrangements;A thorough investigation of mode localization, frequency passbands and stopbands, structural and acoustic intensities and radiated acoustic power is presented for analysis of submerged infinite ribbed plates, with variable rib materials geometry and spacing (periodic and non-periodic). A second investigation of localized natural modes is demonstrated for analysis and experiment of finite stiffened beams in air.