Youhe Zhou

Active control of nonlinear piezoelectric circular shallow spherical shells

Abstract Nonlinear electromechanics and active control of a piezoelectric laminated circular spherical shallow shell are quantitatively investigated in this paper. It is assumed that the piezoelectric layers are uniformly distributed on the top and the bottom surfaces of the shell and the thickness of piezoelectric layers is much thinner than that of the shell. The governing equations for the nonlinear dynamics of active control of the circular spherical shallow shell with piezoelectric actuator are formulated and a semi-analytical method is employed to solve the nonlinear governing equations. The numerical results show that the configuration of nonlinear deformation and the natural frequency of the shell structures can be actively controlled by means of high control voltages across the piezoelectric layers and the jumping phenomenon may occur for the case of geometrical parameter γ= 3 1−μ 2 1/2 f/h ⩾ 1 . In addition the effect of large amplitude on the vibrating frequency is discussed by the Galerkin method and the KBM perturbation.

A general expression of magnetic force for soft ferromagnetic plates in complex magnetic fields

Abstract The experiments of ferromagnetic plates in different magnetic environments exhibit two distinct phenomena, i.e. the magnetoelastic instability of a ferromagnetic plate in transverse magnetic fields, and the increase of natural frequency of a ferromagnetic plate with low susceptibility in an inplane magnetic field. Although these two typical phenomena can be predicted separately by two kinds of theoretical models in which the magnetic forces are formulated by totally different expressions, no theoretical model has been found to commonly describe them. This makes it difficult to predict theoretically magnetoelastic interaction of a ferromagnetic structure in complex magnetic environment. A variational principle, here, is proposed to establish the governing equations of magnetoelastic interaction for soft ferromagnetic thin plate structures under complex magnetic fields. The functional is chosen as the summation of the magnetic energy and the strain energy as well as the external work from applied magnetic fields. From manipulations of the variational principle, the governing equations of the magnetic field and mechanical deformation together with an expression of equivalent magnetic force exerted on the ferromagnetic plates are obtained. It is shown that this theoretical model can commonly characterize the experimental phenomena of the magnetoelastic interaction aforementioned.

Active vibration control of nonlinear giant magnetostrictive actuators

A nonlinear constitutive model-based vibration control system for giant magnetostrictive actuators (Terfenol-D) is presented in this paper. Such actuators utilize the realignment of magnetic moments in response to applied magnetic fields to generate strains in the material. It has been found that the strains and forces generated in this manner are significantly larger than those produced by many other smart materials, associated with significant and complex nonlinear relations among the quantities of applied magnetic field, strain, and compressive pre-stress. Based on the negative feedback control law and the analytical expressions of the nonlinear constitutive model of Terfenol-D rods, here, the effectiveness of real control systems for suppressing a vibration is confirmed by the simulation results on a case study of negative velocity feedback when its feedback gain is taken in a limit region. It is found that the limit region is dependent on the bias magnetic field and pre-stress. When the gain is employed out of the limit region, the real control system is unstable, but the simulation results on the basis of the linear constitutive model still show a stability of the control systems. To utilize the full potential of these materials in active vibration controls, thus, these inherent nonlinearities of the materials must be considered in the design of the control systems.

Drift of Levitated/Suspended Body in High-

Levitation drift in the high-Tc superconducting levitation systems is directly related to the safe operation of the systems. In these levitation systems, the gap between a superconductor and a permanent magnet may decrease, increase, or keep unvarying with time. Based on the numerical simulations of the magnetic force-gap hysteresis relations of two different physical processes in field cooling, and the dynamic features at some given positions on major magnetic force-gap loops, a criterion described by the slopes of the given position on minor and major loops is proposed in this study. According to the suggested criterion, the drift phenomenon can be characterized by judging gap varying with time for a given levitation system. In addition, the characteristic of continuous space range of the equilibrium position of levitated/suspended body has been further exhibited from the numerical results.

T_{c}

Significant flux creep may be generated in some high-T/sub c/ superconductors with weak pinning, which could yield an influence on the dynamic behavior of a high-T/sub c/ superconductor-magnet levitation system. To investigate this influence, this article presents a numerical analysis of dynamic features of the levitation generated by an interaction between a high-T/sub c/ superconductor (HTSC) and a permanent magnet (PM) after the flux creep in the superconductor is taken into account in a macro-model of superconductivity. The influence is comprehensively displayed by comparing the predictions of dynamic responses of such systems in which the flux creep in the superconductor is and is not taken into account. The obtained results show that whether or not the flux creep results in a noticeable influence to the levitation of superconductor-magnet systems is mainly dependent upon properties of superconductivity and applied excitation, e.g., critical current density of superconductors, and amplitude and frequency of external excitations. When the critical current density is less than 4.5/spl times/10/sup 8/ A/m/sup 2/, and the system is subjected to a periodic excitation, the influence of flux creep should be taken into account in the theoretical analysis.

Superconducting Levitation Systems Under Vibration—Part I: A Criterion Based on Magnetic Force-Gap Relation for Gap Varying With Time

We report a phonon transport model for a bulk thermoelectric material to investigate the effect of the grain diameter and the grain-boundary thickness on its thermal conductivity. The analysis results display that the bulk thermal conductivity is significantly reduced by decreasing the grain sizes when the grain diameter is less than 500nm, which provides us one feasible way to enhance the figure of merit ZT of the material, and the thermal conductivity is mainly attributed to the contribution of grains, while the grain-boundary thermal conductivity has to be considered when the grain diameter is less than 100nm.

Influence of flux creep on dynamic behavior of magnetic levitation systems with a high-T/sub c/ superconductor

The stress and magnetostriction induced by flux pinning for a flat superconducting strip of a type II superconductor are calculated analytically in the presence of transport current. The plane stress approach is used to find the exact solutions. By assuming that the current density is magnetic field independent, the body force and normal stress distributions for increasing and decreasing transport currents are given. In addition, the pinning induced magnetostriction is calculated. The results show that, during the transport current reduction, tensile stress may occur. It is worth pointing out that, in the flat superconducting strip with transport current, the stresses are mainly negative. The hysteresis loop of the magnetostriction cannot be observed for the full cycle of the transport current.

Impact of grain sizes on phonon thermal conductivity of bulk thermoelectric materials

Magnetoelastic effects, which are caused by flux pinning in the superconductors, often induce fatal cracking of the bulk high temperature superconductors (HTS). In the present work, the Kim model is considered for the critical state in which the critical current density is assumed to depend on the flux density. Based on the plane strain approach, the analytic expression of the stress under the magnetic field is derived for a specimen having a slab geometry and infinitely along the other two directions. The stress field is obtained in the slab for the Kim model, and the stress behavior is discussed for two magnetization processes: the decreasing field and the field cooling. It is shown that the effects of the parameter p on the stress are related to the magnetization process. Compared to the Bean model, the results for the Kim model show the same trend with respect to the external field Ba during field cooling. Generally speaking, these results are of clear interest to experimentalists and to the successfu...

Stress distribution in a flat superconducting strip with transport current

In this article, the dependence of effective magnetostriction of the bulk superconductors on the parameters including the elastic moduli and volume fraction is investigated. For a bulk superconductor of nonsuperconducting particles dispersed in a superconducting matrix, a simple and approximate model for effective magnetostriction is described. Based on the plane strain approach, the two-dimensional magnetostriction is obtained by implementing the continuity conditions of displacement and stress at the interface between the particle and the matrix. The results obtained show that the elastic moduli and volume fraction have obvious effects on the magnetostriction of bulk superconductors, which may explain why the experimental and the theoretical results have small differences.

Kim model of stress induced by flux pinning in type-II superconductors

To study levitation drift further, i.e., the gap between a superconductor and a permanent magnet varying with time in high-Tc superconducting levitation systems, drift velocity is introduced. Based on the numerical simulations of the dynamic response of a levitated body, and according to the essential reasons for drift, the drift velocity is first divided into two regimes: Vff [related to flux flow (FF)] and Vtc [related to flux creep (FC)]. The drift velocity is shown to be mainly dependent upon properties of superconductivity (such as the critical current density of superconductors), initial disturbances, and applied excitations (such as the amplitude and the frequency of external excitations). Furthermore, the corresponding influences of the drift velocities Vff and Vfc have been investigated quantitatively in this paper.