横向磁场中旋变运动导电圆板的参强联合共振

Magnetoelastic resonance of a conductive circular plate rotating with varying velocity under combined parametric and forced excitations

研究变速旋转圆板的非线性磁弹性参强联合振动问题。给出旋转圆板在磁场中的磁弹性振动方程,应用伽辽金法离散变量,得到横向磁场中旋转圆板轴对称参强联合振动微分方程。运用多尺度法求解振动微分方程,分析久期项得到系统发生参强联合共振时的两种共振状态,并分别给出两种状态下系统的幅频响应方程。通过数值计算,给出圆板的协调参数、磁场、转速、激励力等参数变化对振动特性的影响,对比两种共振条件下的幅值-参数曲线,讨论不同参数变化对系统稳定性的影响。通过系统的全局分岔图,讨论分岔参数变化对系统动力学特性的影响。

Magneto-elastic resonance of a conductive circular plate rotating with varying velocity under combined parametric and forced excitations was investigated. The conductive circular plate was subjected to parametric excitations due to the time-varying rotating speed and magnetic field forces. The magneto-elastic parametric vibration equations of the variable-velocity rotating conductive circular plate were established,its axisymmetric vibration differential equation under combined parametric and forced excitations was obtained through the application of Galerkin method. Then,the multiscale method was applied to derive two conditions for resonance occurring,two corresponding amplitude-frequency response equations were deduced,respectively. The influences of plate ＇s coordination parameters, magnetic field parameters,rotating speed and excitations on the vibration performance of the circular plate were studied. Amplitudeparameter curves of two resonance conditions were compared,and the influences of parameters on the system＇s stability were discussed. According to the global bifurcation diagram of the system,the influences of changes of bifurcation parameters on the system dynamic characteristics were discussed.