Modeling of Non-Linear and Hysteretic Magnetization Effects in Transient Potential Drop Measurements

We have compared transient potential drop measurements on ferromagnetic steel rods with finite difference simulation assuming that the magnetization varies as a quadratic function of the applied field. Good agreement between simulation and experimental measurement is achieved and the results are discussed in terms of the Rayleigh law of magnetization.

Development of a Material Constitutive Model and Simulation Technique to Predict Nonlinearities in Piezoelectric Materials under Weak Electric Fields

Piezoceramic materials exhibit different types of nonlinearities depending upon the magnitude of the mechanical and electric field strength in the continuum. Some of the nonlinearities observed under weak electric fields are: presence of superharmonics in the response spectra and jump phenomena etc. especially if the system is excited near resonance. It has also been observed by many researchers that, at weak alternating stress fields, the relationship between the piezoelectrically induced charge and applied stress in ferroelectric ceramics, has the same form as the Rayleigh law (for magnetization versus magnetic field) in ferromagnetic materials. Applicability of the Rayleigh law to the piezoelectric effect has been demonstrated for Lead Zirconate Titanate ceramics by many researchers and their experimental results indicate that the dominant mechanism responsible for piezoelectric hysteresis and the dependence of the piezoelectric coefficient on the applied alternating stress is the pinning of non-180° domain walls. In this chapter, the Rayleigh law for ferromagnetic hysteresis has been modified and incorporated in a nonlinear electric enthalpy function and then applied in the analysis of hysteresis behavior of piezoelectric continua. Analytical solutions have been derived for a cantilever beam actuated by two piezo-patches attached to the top and bottom of the beam and excited by opposite electric fields. Analysis has been carried out at different electric field excitations of varying amplitude and frequencies and the results have been compared with the available experimental results from literature.

Nonlinear Dielectric and Piezoelectric Responses in (Bi, La)FeO3-Pb(Ti, Mn)O3 Ceramics

ABSTRACTPolycrystalline solutions of 0.6(Bi0.9La0.1)FeO3-0.4Pb(Ti1-xMnx)O3(BLF-PTM, x=0 and 0.01)have been fabricated by the so-gel process combined with a solid state reaction method. BLF-PTM exhibits the nonlinear dielectric and piezoelectric responses under applied fields. Rayleigh law has been used to evaluate the irreversible contribution of the domain walls movement to the nonlinear dielectric response. Rayleigh analysis reveals that a mechanism with no associated loss exists in the BLF-PTM of x=0.01. The real part piezoelectric coefficient of BLF-PTM linearly increases with increasing the electric fields. The dielectric and piezoelectric nonlinear coefficient of 0.17×10-3 m/V and 0.897 ×10-17 m2/V2 respectively are obtained for BLF-PTM of x=0.01,which are smaller than those of 0.22×10-3 m/V and 1.19 ×10-17 m2/V2 for BLF-PTM of x=0. Our results indicate that Mn doping increase the intrinsic piezoelectric properties of BLF-PTM reducing the extrinsic contributions to piezoelectric responses.

Nonlinear Crest Height Distribution in Three-Dimensional Ocean Waves

The interest and the studies on nonlinear waves are increased recently for their importance in the interaction with floating and fixed bodies. It is also well known that nonlinearities influence wave crest and wave trough distributions, both deviating from Rayleigh law. In this paper a theoretical crest distribution is obtained taking into account the extension of Boccotti’s Quasi Determinism theory, up to the second order for the case of three-dimensional waves, in finite water depth. To this purpose the Fedele & Arena [2005] distribution is generalized to three-dimensional waves on an arbitrary water depth. The comparison with Forristall second order model shows the theoretical confirmation of his conclusion: the crest distribution in deep water for long-crested and short crested waves are very close to each other; in shallow water the crest heights in three dimensional waves are greater than values given by long-crested model.