Magnetoelastic combined resonance and stability analysis of a ferromagnetic circular plate in alternating magnetic field

The nonlinear combined resonance problem of a ferromagnetic circular plate in a transverse alternating magnetic field is investigated. On the basis of the deformation potential energy, the strain potential energy, and the kinetic energy of the circular plate, the Hamilton principle is used to induce the magnetoelastic coupling transverse vibration dynamical equation of the ferromagnetic circular plate. Based on the basic electromagnetic theory, the expressions of the magnet force and the Lorenz force of the circular plate are presented. A displacement function satisfying clamped-edge combined with the Galerkin method is used to derive the Duffing vibration differential equation of the circular plate. The amplitude-frequency response equations of the system under various combined resonance forms are obtained by means of the multi-scale method, and the stability of the steady-state solutions is analyzed according to the Lyapunov theory. Through examples, the amplitude-frequency characteristic curves with different parameters, the amplitude of resonance varying with magnetic field intensity and excitation force, and the time-course response diagram, phase diagram, Poincar′e diagram of the system vibration are plotted, respectively. The effects of different parameters on the amplitude and stability of the system are discussed. The results show that the electromagnetic parameters have a significant effect on the multi-valued attribute and stability of the resonance solutions, and the system may exhibit complex nonlinear dynamical behavior including multi-period and quasi-periodic motion.

Principal and internal resonance of rectangular conductive thin plate in transverse magnetic field

The principle and 1:3 internal resonance of a rectangular thin plate in a transverse magnetic field is investigated.Based on the magneto-elastic vibration equation and electromagnetic force expressions of the thin plates,the nonlinear magneto-elastic vibration differential equations of rectangular plates under external excitation in a transverse magnetic field are derived.For a rectangular plate with one side fixed and three other sides simply supported,the two-degree-offreedom nonlinear Duffing vibration differen-tial equations are proposed by the method of Galerkin.The method of multiple scales is adopted to solve the model equations and obtain four first-order ordinary differential equations governing modulation of the amplitudes and phase angles involved via the first-order or the second-order primary-internal reso-nances.With a numerical example,the amplitude frequency response curves,time history responses,phase portraits and Poincare maps of the first two order vibration modes via principle-internal resonance are respectively captured.And the effects of external excitation amplitudes,magnetic field intensities and thicknesses on the vibration of system are discussed.The results show that the response is dominated by the low mode when principle-internal resonance occurs.The internal resonance provides a mechanism for transferring energy from a high mode to a low mode.

热环境中旋转运动功能梯度圆板的强非线性固有振动

研究热环境中旋转运动功能梯度圆板的非线性固有振动问题.针对金属-陶瓷功能梯度圆板,考虑几何非线性、材料物理属性参数随温度变化以及材料组分沿厚度方向按幂律分布的情况,应用哈密顿原理推得热环境中旋转运动功能梯度圆板的非线性固有振动方程组.考虑周边夹支边界条件,利用伽辽金法得到了圆板的横向非线性微分方程,并确定了静载荷引起的静挠度.考虑到固有振动微分方程具有强非线性的特点,采用改进的多尺度法进行求解,得出非线性固有频率表达式.通过算例,分析了旋转运动功能梯度圆板固有频率随转速、温度等参量的变化情况.将论文退化结果与现有文献所得解进行对比,并将龙格-库塔法和周期图法所得数值解与论文的解析解进行了比较,结果是吻合的.结果表明,非线性固有频率随金属含量的增加而降低;随转速和圆板厚度的增大而升高;随功能梯度圆板表面温度的升高而降低,且当金属、陶瓷表面温度同时升高时,非线性固有频率下降的更快.给出的固有频率和位移解对于功能梯度结构的动力特性分析具有参考意义.

Magnetic-structure coupling dynamic model of a ferromagnetic plate parallel moving in air-gap magnetic field

Aiming at the air-gap magnetic field excited by wall armatures,Laplace’s partial differential equation of air-gap magnetic potential is achieved by means of the electromagnetic field theory.According to the magnetic boundary conditions and the method of separation of variables,the magnetic potential of the air-gap magnetic field is obtained.Based on the magnetization force model and Lorentz force of ferromagnetic thin-walled structures,and introducing the electromagnetic constitutive relations and boundary conditions,the calculation model of electromagnetic force of the soft ferromagnetic thin plate moving in air-gap magnetic field is established.Considering geometric nonlinearity,expressions of strain energy and kinetic energy of the elastic thin plate and the work of forces are given,respectively.The magnetic-structure coupling nonlinear vibration equations of ferromagnetic thin plate parallel moving in the air-gap magnetic field excited by armatures are obtained by using the Hamilton principle,which can be of the characterization of the system dynamics model with electro-magneto-velocity-mechanical interaction.Through numerical examples,primary resonance characteristics of the strip thin plate under the action of air-gap magnetic force are obtained.The results show that the two stable amplitude values will increase as amplitude of magnetic potential increases and thickness of air-gap decreases,and the amplitude’s multi-valued region will change due to the varieties of magnetic potential,air-gap and velocity.The model established in this paper is a theoretical reference for investigation on the multi-field coupling dynamic behaviors of structures moving in complex electromagnetic fields.

SOME RATIONALITY CONDITIONS OF JOINT EFFICIENT MAPPING IN GROUP MULTI-OBJECTIVE PROGRAMMING

The joint efficient ordering method is a fundamental method of ordering alternatives in group multi-objective programming problems. In this paper, the rational properties of the joint efficient mapping corresponding to the joint efficient ordering method are studied, and some necessary conditions of this mapping are proven.

Paradox of voting and the trivial preference set of groupdecision making

The structure of the trivial preference set of group decision making is studied, and the essential characters and generating reasons of the paradox of voting are revealed.