电磁与机械载荷作用下导电梁式板的超谐波共振
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Ultraharmonic resonance of conductive beam-plate under magnetic field and mechanic loading
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    摘要:

    研究了电磁与机械载荷共同作用下梁式薄板的非线性超谐波共振问题。在给出薄板的电磁弹性运动基本方程及电磁力表达式的基础上,推得了横向稳恒磁场和机械载荷共同作用下梁式薄板的振动方程;应用伽辽金积分法,进一步导出了相应的非线性振动控制微分方程.采用多尺度法进行求解,得到了稳态运动下的幅频响应方程.最后,通过算例,给出了相应的幅频响应曲线图和时间历程图,分析了板厚、磁场及激励幅值对系统振动的影响.

    Abstract:

    In this paper, the non-linear ultraharmonic resonance of a conductive beam plate in a magnetic field subjected to some mechanical loadings is studied. Base on nonlinear electro-magneto-elastic equations of the plate and the expression of electromagnetic forces, the vibration equations of thin beam plate under uniform transverse magnetic field and mechanical loadings are obtained. By use of the Galerkin’s method, the differential equation of the nonlinear vibration is derived consequently. By mean of multiscale method, the amplitude and frequency resonance equations in steady state are arrived at. By some examples, the amplitude-frequency curves, time history curves are derived. The influences of plate thickness, magnetic field and excitation amplitude on vibration properties of system are analyzed.

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胡宇达,杜国君,王国伟.电磁与机械载荷作用下导电梁式板的超谐波共振[J].动力学与控制学报,2004,2(4):35~38; Hu Yuda, Du Guojun, Wang Guowei. Ultraharmonic resonance of conductive beam-plate under magnetic field and mechanic loading[J]. Journal of Dynamics and Control,2004,2(4):35-38.

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  • 收稿日期:2004-09-28
  • 最后修改日期:2004-10-27
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