Combined Parametric and Forced Resonance of Axially Moving and Current-Carrying Beams Under Moving Loads
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摘要: 研究磁场环境中移动载荷作用下轴向运动梁的磁弹性参强联合共振问题.以轴向运动载流梁为研究对象,建立横向磁场中受移动载荷作用下梁的力学模型.应用Hamilton(哈密顿)原理,得到梁的非线性磁弹性振动方程.利用Galerkin(伽辽金)积分法和多尺度法,推得以移动载荷为变量的幅频响应方程.通过数值计算,绘制了振幅随调谐参数、拉力扰动幅值、移动载荷、磁感应强度的变化规律曲线图,分析了电流密度、磁感应强度、移动载荷等变量对参变系统动力学特性的影响.结果表明:系统呈现典型的参强联合共振特性;移动载荷、磁感应强度能够起到抑制共振幅值多值现象的产生.Abstract: The combined parametric and forced resonance of axially moving beams subjected to moving loads in magnetic field environment was investigated. For an axially moving and current-carrying beam, the mechanical model under moving load in the magnetic field was established. The Hamiltonian variational principle was applied to formulate the nonlinear magnetoelastic vibration equations. By means of the Galerkin integral method and the multiscale method, the nonlinear primary parametric amplitude-frequency response equations were achieved with the moving load as a variable. The curves of the amplitude changing with the tuning parameters, the tension disturbance, the moving load, the magnetic induction intensity and the moving load length were drawn. The influences of the axial tension, the moving load and other parameters on the dynamic behaviors of the parametric system were analyzed through numerical calculation. The results show that the system presents typical nonlinear vibration characteristics; moreover, the moving load and the magnetic field control the occurrence of the multi-value amplitude phenomenon.
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