Magnetoelastic Vibration And Stability Of A Circular Plate In Induced Magnetic Field

As core components in engineering structure,circular and annular plate structures are widely used in many fields such as aerospace,electric power engineering,and machining.The research on vibration and stability of conductive plate structures working in complex multi-physics fields has become a frontier that causes attention.Many studies on electromagnetic mechanics are still in stage of theoretical exploration.Many theoretical assumptions and computational models still need to be deepened and improved.The vibration and motion of plate structure will form coupling effect between motion and electromagnetic,and significantly affect the natural vibration characteristics of structure.When external disturbance excitation or noise exists,resonance may be excited,resulting in structural deformation or even instability and failure.It is important to avoid resonance and ensure safe operation.In this paper,the magnetoelastic natural vibration and stability of conductive circular and annular plate in the induced magnetic field of current-carrying wire are studied,where the inherent change law of system nonlinear vibration and coupling relationship under various complex magnetic field environments is analyzed.Based on assumption of Kirchhoff thin plate theory and considering influence of geometric nonlinearity,the expressions of kinetic energy,potential energy and virtual work of external force on virtual displacement for circular plate are derived.By deriving spatial distribution of induced magnetic field for different current-carrying coils and combining Maxwell’s electromagnetic field theory and electromagnetic constitutive relations,the expressions of electromagnetic force and electromagnetic torque containing current terms are obtained.The nonlinear magnetoelastic coupling control equations of circular plate is derived by Hamilton variational principle.The magnetoelastic natural vibration of a conducting circular plate in uniform magnetic field induced by current-carrying three parallel coaxial coils and spherical coils is studied.For plate with clamped and simply supported boundary conditions,the axisymmetric linear vibration differential equation is obtained by Galerkin method.The characteristic diagrams of vibration and electromagnetic of plate are obtained,where variation of natural frequency,damping ratio and electromagnetic torque with current density,number of coil turns and plate geometry size are analyzed.The magnetoelastic natural vibration of a circular plate in a non-uniform magnetic field induced by a current-carrying circular coil is presented.The elliptic integral expression of induced non-uniform magnetic field and electromagnetic force are deduced,and natural frequency of plate is derived.Through numerical calculation,the magnetoelastic natural vibration characteristic curves are obtained for plate with clamped and simply supported boundary conditions.The effects of coil current intensity,plate size on vibration characteristics under non-uniform magnetic field environment are discussed.The nonlinear vibration of circular plates in the non-uniform magnetic field induced by current-carrying circular coil is studied.Considering geometric nonlinearity effect,the nonlinear vibration differential equation is derived,which is solved by multi-scale method,then the nonlinear frequency and singularity stability criterion of the dynamic system are obtained.Through numerical calculation,the nonlinear vibration characteristic curves of plate under non-uniform magnetic field is obtained.The influence of coil current on nonlinear frequency,deflection,response,and complex changing law of electromagnetic characteristics under non-uniform magnetic field are discussed.Combined with stability criterion,the change mechanism of system singularity stability is revealed.The nonlinear natural vibration of an annular plate in non-uniform toroidal magnetic field excited by current-carrying straight wire is presented.The expressions of induced magnetic field and electromagnetic forces are obtained.The displacement function of plate satisfying three different boundary conditions is solved and the magnetoelastic axisymmetric vibration differential equation is deduced.By utilizing the multi-scale method,one obtains the analytical solution.Through numerical calculation,influence of different parameters such as wire current and size effect on natural frequency and electromagnetic force are analyzed.The variation law of system singularity stability with different control parameters is disscussed.The non-axisymmetric nonlinear coupling vibration of annular plates in induced non-uniform toroidal magnetic field is achieved.The electromagnetic force expression under multi-modal coupling effect and non-axisymmetric nonlinear vibration differential equations are derived.The multi-scale method is employed to obtain natural frequency expression of multi-order coupling form of system.Through programming calculation,the variation law curves of multi-order natural frequency and electromagnetic characteristics of system are obtained,which reveals the influence of coupling effect between modes and geometric nonlinearity on multi-order frequency when external current,initial conditions,time and other parameters vary.The response diagram and phase diagram of the first three orders of system are drawn numerically,and the variation law of singularity and phase trajectory is analyzed.