【摘要】 研究了磁场环境中受机械载荷作用梁式薄板的非线性主共振问题。在给出薄板的非线性电磁弹性耦合运动基本方程及电磁力表达式的基础上,得到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,并进行无量纲化处理,进一步导出了相应的非线性振动微分方程。采用平均法对主共振问题进行了求解,得到了稳态运动下的幅频响应方程。通过算例给出了几种情况下的幅频响应曲线图和时间历程图,分析了板厚和磁场对系统振动的影响。更多还原

【Abstract】 The non-linear principal resonance of a conductive beam plate in a magnetic field subjected to some mechanical loadings is studied.Base on nonlinear electro-magneto-elastic soupled dynamic equations of the plate and the expression of electromagnetic forces,the vibration equations of the thin beam plate under uniform transverse magnetic field and mechanical loadings are obtained.By use of the Galerkin method,combined with non-dimensional method,the differential equation of the nonlinear vibration is derived consequently.By mean of averaging method,the amplitude-frequency response equations in steady state are obtained.By some examples,the amplitude-frequency response curves and the relevant time history curves are given.The influences of plate thickness and magnetic field on the vibration behavior of the system are analyzed.更多还原