Magneto-elastic combination resonances analysis of current-conducting thin plate

Based on the Maxwell equations, the nonlinear magneto-elastic vibration equations of a thin plate and the electrodynamic equations and expressions of electromagnetic forces are derived. In addition, the magneto-elastic combination resonances and stabilities of the thin beam-plate subjected to mechanical loadings in a constant transverse magnetic filed are studied. Using the Galerkin method, the corresponding nonlinear vibration differential equations are derived. The amplitude frequency response equation of the system in steady motion is obtained with the multiple scales method. The excitation condition of combination resonances is analyzed. Based on the Lyapunov stability theory, stabilities of steady solutions are analyzed, and critical conditions of stability are also obtained. By numerical calculation, curves of resonance-amplitudes changes with detuning parameters, excitation amplitudes and magnetic intensity in the first and the second order modality are obtained. Time history response plots, phase charts, the Poincare mapping charts and spectrum plots of vibrations are obtained. The effect of electro-magnetic and mechanical parameters for the stabilities of solutions and the bifurcation are further analyzed, Some complex dynamic performances such as perioddoubling motion and quasi-period motion are discussed.

Magneto-elastic dynamics and bifurcation of rotating annular plate

In this paper, magneto-elastic dynamic behavior, bifurcation, and chaos of a rotating annular thin plate with various boundary conditions are investigated. Based on the thin plate theory and the Maxwell equations, the magneto-elastic dynamic equations of rotating annular plate are derived by means of Hamilton＇s principle. Bessel function as a mode shape function and the Galerkin method are used to achieve the transverse vibration differential equation of the rotating annular plate with different boundary conditions. By numerical analysis, the bifurcation diagrams with magnetic induction, amplitude and frequency of transverse excitation force as the control parameters are respectively plotted under different boundary conditions such as clamped supported sides, simply supported sides, and clamped-one-side combined with simply-anotherside. Poincare′ maps, time history charts, power spectrum charts, and phase diagrams are obtained under certain conditions,and the influence of the bifurcation parameters on the bifurcation and chaos of the system is discussed. The results show that the motion of the system is a complicated and repeated process from multi-periodic motion to quasi-period motion to chaotic motion, which is accompanied by intermittent chaos, when the bifurcation parameters change. If the amplitude of transverse excitation force is bigger or magnetic induction intensity is smaller or boundary constraints level is lower, the system can be more prone to chaos.

Surface effect on band structure of magneto-elastic phononic crystal nanoplates subject to magnetic and stress loadings

This paper presents a theoretical model for the size-dependent band structure of magneto-elastic phononic crystal(PC)nanoplates according to the Kirchhoff plate theory and Gurtin-Murdoch theory,in which the surface effect and magneto-elastic coupling are considered.By introducing the nonlinear coupling constitutive relation of magnetostrictive materials,Terfenol-D/epoxy PC nanoplates are carried out as an example to investigate the dependence of the band structure on the surface effect,magnetic field,pre-stress,and geometric parameters.The results show that the surface effect has promotive influence on dispersion curves of the band structure,and the band gaps can be improved gradually with the increase in the material intrinsic length.Meanwhile,the band gaps exhibit obvious nonlinear coupling characteristics owing to the competition between the magnetic field and the pre-stress.By considering the surface effect and magneto-elastic coupling,the open and closed points of band gaps are found when the lattice constant to thickness ratio increases.The study may provide a method for flexible tunability of elastic wave propagation in magneto-elastic PC nanoplates and functional design of highperformance nanoplate-based devices.

Numerical Analysis on the Magneto-Elastic Stability of Current-Carrying Conductors: Aiming at Applications for the Tokamak System

A novel method for calculating the magnetic stiffness matrix was proposed for the numerical analysis of the magneto-elastic stability of complicated current-carrying structures aim- ing for application in the magneto-elastic behavior of the tokamak system. A code based on the proposed method was developed and applied to the numerical analysis of two typical current- carrying structures. The good consistency of the numerical and analytical results validated the proposed method and the related numerical code.

Principal parametric resonance of axially accelerating rectangular thin plate in magnetic field

Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying speed in the magnetic field. Consid- ering geometric nonlinearity, based on the expressions of total kinetic energy, potential energy, and electromagnetic force, the nonlinear magneto-elastic vibration equations of axially moving rectangular thin plate are derived by using the Hamilton principle. Based on displacement mode hypothesis, by using the Galerkin method, the nonlinear para- metric oscillation equation of the axially moving rectangular thin plate with four simply supported edges in the transverse magnetic field is obtained. The nonlinear principal parametric resonance amplitude-frequency equation is further derived by means of the multiple-scale method. The stability of the steady-state solution is also discussed, and the critical condition of stability is determined. As numerical examples for an axially moving rectangular thin plate, the influences of the detuning parameter, axial speed, axial tension, and magnetic induction intensity on the principal parametric resonance behavior are investigated.

Insights into the regulation mechanism of ring-shaped magnetoelectric energy harvesters via mechanical and magnetic conditions

This paper presents a theoretical model for predicting and tuning magnetoelectric(ME)effect of ring-shaped composites,in which stress boundary conditions are empoyed and the multi-field coupling property of giant magnetostrictive materials are taken into account.A linear analytical solutions for the closed-and open-circuit ME voltages are derived simultaneously using mechanical differential equations,interface and boundary conditions,and electrical equations.For nonlinear ME coupling effect,the nonlinear multi-field coupling constitutive equation is reduced to an equivalent form by expanding the strains as a Taylor series in the vicinity of bias magnetic field.Sequentially,the linear model is generalized to a nonlinear one involving the field-dependent material parameters.The results show that setting a stress-free condition is beneficial for reducing resonance frequency while applying clamped conditions on the inner and outer boundaries may improve the maximum output power density.In addition,performing stress conditions on one of the boundaries may enhance ME coupling significantly,without changing the corresponding resonance frequency and optimal resistance.When external stimuli like bias magnetic field and pre-stress are applied to the ring-shaped composites,a novel dual peak phenomenon in the ME voltage curve around resonance frequencies is revealed theoretically,indicating that strong ME coupling may be achieved within a wider bias field region.Eventually,the mutual coordination of the bias field and pre-stress may enhance ME coupling as well as tuning the resonance frequency,and thus is pivotal for tunable control of ME energy harvesters.The proposed model can be applied to design high-performance energy harvesters by manipulating the mechanical conditions and external stimuli.

AN ANALYSIS FOR IMPERFECT SENSITIVITY OF A SUPERCONDUCTING ROD

On the basis of the interaction between the electromagnetic field and a solid, the imperfect sensitivity of a superconducting rod is studied in this paper. The influences of the initial deflection of the rod and the initial magnetic field on the stability are discussed. One can see that the bifurcation response of the rod with imperfections is similar to the universal unfolding of the fork bifurcation from the singularity theory.

Anisotropic magnetoelastic response in the magnetic Weyl semimetal Co_(3)Sn_(2)S_(2)

Co_(3)Sn_(2)S_(2) is a recently identified magnetic Weyl semimetal in Shandite compounds. Upon cooling, Co_(3)Sn_(2)S_(2) undergoes a ferromagnetic transition with c-axis polarized moments(0.3 μ_(B)/Co) around T_(C)= 175 K, followed by another magnetic anomaly around T_(A)≈ 140 K. A large intrinsic anomalous Hall effect is observed in the magnetic state below TC with a maximum of anomalous Hall angle near T_(A). Here, we report an elastic neutron scattering on the crystalline lattice of Co_(3)Sn_(2)S_(2) in a magnetic field up to 10 T. A strongly anisotropic magnetoelastic response is observed, while only a slight enhancement of the Bragg peaks is observed when B//c. The in-plane magnetic field(B//ab) dramatically suppresses the Bragg peak intensity probably by tilting the moments and lattice toward the external field direction. The in-plane magnetoelastic response commences from T_(C), and as it is further strengthened below T_(A), it becomes nonmonotonic against the field between T_(A) and T_(C) because of the competition from another in-plane magnetic order. These results suggest that a magnetic field can be employed to tune the Co_(3)Sn_(2)S_(2) lattice and its related topological states.