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 ...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.展开更多
This paper presents analytical solutions for full-field radiation in magnetoelectric(ME)antennas,considering a fully magnetoelastic coupled constitutive relation.A nonlinear converse ME coupling model is established,i...This paper presents analytical solutions for full-field radiation in magnetoelectric(ME)antennas,considering a fully magnetoelastic coupled constitutive relation.A nonlinear converse ME coupling model is established,incorporating mechanical,electric,and magnetic variables with generalized Maxwell equations.This model emphasizes the essence of ME antennas,where radiation is achieved through strain/stress-mediated coupling between different phases.The magnetic flux density and electric displacement obtained from the model are used as sources to solve the full-field radiations of ME antennas.The proposed model is validated through existing experiments and simulations,demonstrating that the radiation performance of ME antennas is strongly influenced by nonlinear magneto-elastic coupling.The material parameters and magnetic bias significantly impact the magnetic flux density and far-field radiation due to the nonlinear magnetization process.The study reveals the mechanisms behind enhanced working bandwidth and frequency tuning by examining the frequency response of the radiation impedance with material parameters.By adjusting the initial magnetization rate,saturation magnetostriction,and saturation magnetization,the radiation efficiency/gain can be increased by 340%,108%,and 112%respectively.This model enhances our understanding of the full-field radiation of ME antennas and provides a foundation for designing tunable ME antennas.展开更多
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...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.展开更多
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-elasti...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.展开更多
基金supported by the Natural Science Foundation of Hebei Province of China(No.E2010001254)
文摘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.
基金supported by the Natural Science Foundation of Shaanxi Province(Grant No.2024JC-YBMS-069)the Fundamental Research Funds for the Central Universities and the Innovation Fund of Xidian University(Grant Nos.ZYTS24026 and YJSJ24001).
文摘This paper presents analytical solutions for full-field radiation in magnetoelectric(ME)antennas,considering a fully magnetoelastic coupled constitutive relation.A nonlinear converse ME coupling model is established,incorporating mechanical,electric,and magnetic variables with generalized Maxwell equations.This model emphasizes the essence of ME antennas,where radiation is achieved through strain/stress-mediated coupling between different phases.The magnetic flux density and electric displacement obtained from the model are used as sources to solve the full-field radiations of ME antennas.The proposed model is validated through existing experiments and simulations,demonstrating that the radiation performance of ME antennas is strongly influenced by nonlinear magneto-elastic coupling.The material parameters and magnetic bias significantly impact the magnetic flux density and far-field radiation due to the nonlinear magnetization process.The study reveals the mechanisms behind enhanced working bandwidth and frequency tuning by examining the frequency response of the radiation impedance with material parameters.By adjusting the initial magnetization rate,saturation magnetostriction,and saturation magnetization,the radiation efficiency/gain can be increased by 340%,108%,and 112%respectively.This model enhances our understanding of the full-field radiation of ME antennas and provides a foundation for designing tunable ME antennas.
基金Project supported by the National Natural Science Foundation of China(Grant No.11472239)the Hebei Provincial Natural Science Foundation of China(Grant No.A2015203023)the Key Project of Science and Technology Research of Higher Education of Hebei Province of China(Grant No.ZD20131055)
文摘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.
文摘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.
