传导薄板的非线性磁弹性振动问题

研究了磁场环境中传导薄板的非线性磁弹性振动问题。由虚功原理,给出了磁场中薄板的磁弹性耦合运动方程。并根据薄板薄壳的磁弹性基本假设及麦克斯威尔方程,得到了方程中电磁力及力矩的表达式。作为具体问题,采用多尺度法求出了横向磁场中条形板非线性振动的近似解析解。通过算例,分析了磁场环境对振动周期和幅值的影响。从而证实了,通过改变磁场因素,可达到控制该磁场环境中传导薄板振动的目的。所得的结论,对工程实际将有较大的应用参考价值。

MAGNETO-ELASTIC NONLINEAR VIBRATION ANALYSIS OF A THIN CONDUCTIVE PLATE

The problem of non-linear magneto-elastic vibration is studied in this paper The motion equation of magneto-elastic coupling for a thin plate in the magnetic field is obtained using the principle of virtual work. According to the basic hypothesis of magneto-elasticity and Maxwell field equation, the expressions of electromagnetic force and torque in this equation are given. As an example, an approximate analytic solution of nonlinear vibration for a plate strip in lateral magnetic field is obtained by the multi-scale method. The influence of magnetic intensity on the period and the amplitude of vibration is discussed. It is shown that the vibration of a conductive thin plate under the action of a magnetic field is controllable through adjusting its parameters.