磁场中轴向变速运动载流梁的参强联合共振

发布时间：2018-04-01 21:01

本文选题：载流梁　切入点：主共振-主参数共振　出处：《中国机械工程》2016年23期

【摘要】：研究磁场环境中轴向变速运动载流梁在简谐激励作用下的参强联合共振问题,应用弹性力学理论、电磁场基本理论以及哈密顿变分原理,得到轴向变速运动载流梁的非线性磁弹性耦合振动方程。利用伽辽金积分法对其进行时间变量和空间变量的离散化,进而运用多尺度法以及坐标变换的方法求得系统主共振-主参数共振的幅频响应方程。通过算例,得到了系统随不同参数变化的幅频响应曲线图、时间历程图、相轨迹图、庞加莱映射图和共振系统的动相平面轨迹图,分析了轴向速度、轴向拉力、磁感应强度、电流密度及强迫激励对系统主共振-主参数共振特性的影响,结果表明系统呈现典型的非线性振动特征和复杂的动力学行为。
[Abstract]:In this paper, the problem of parametric joint resonance of an axially variable velocity moving current-carrying beam under harmonic excitation in a magnetic field is studied. The theory of elasticity, the basic theory of electromagnetic field and the Hamiltonian variational principle are applied. The nonlinear magnetoelastic coupling vibration equation of a current-carrying beam with axial variable speed motion is obtained. The Galerkin integration method is used to discretize the time and space variables. The amplitude-frequency response equation of the main resonance and principal parameter resonance of the system is obtained by using the multi-scale method and coordinate transformation method. The amplitude-frequency response curve, the time history diagram and the phase trajectory diagram of the system with different parameters are obtained by an example. The effects of axial velocity, axial tension, magnetic induction intensity, current density and forced excitation on the resonance characteristics of the system are analyzed. The results show that the system presents typical nonlinear vibration characteristics and complex dynamic behavior.
【作者单位】：燕山大学河北省重型装备与大型结构力学可靠性重点实验室;
【基金】：国家自然科学基金资助项目(11472239) 河北省自然科学基金资助项目(A2015203023) 河北省高等学校科学技术研究资助重点项目(ZD20131055)
【分类号】：O327

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