【作者】 孙建涛；

【导师】 胡宇达；

【作者基本信息】 燕山大学 ， 工程力学， 2012， 硕士

【摘要】 随着现代科学技术的高速发展，利用铁磁、导体、压电等材料作为主要构件的电磁装置越来越多应用于工程实际中，使得磁弹性振动问题日益显现。而随着电磁固体力学的发展，电磁场和机械场共同作用下的轴向系统也受到更广泛的关注。因此，有必要进一步开展这方面的研究工作，如何对众多处于电磁场环境下的振动结构进行安全设计和可靠性评估，具有重要的理论和现实意义。本文主要研究了不同边界条件下的轴向运动矩形薄板的磁弹性振动问题。首先，根据电磁理论和麦克斯韦方程组导出了电磁力和电磁力矩，根据薄板理论并运用哈密顿原理推导出了轴向运动矩形薄板的磁弹性振动方程。其次，针对四种不同的边界条件，设定位移函数，并应用伽辽金方法对薄板磁弹性振动方程进行积分，分别导出了轴向运动矩形薄板的自由振动微分方程、受迫振动微分方程。通过对系统振动微分方程进行求解，得到了系统自由振动频率变化规律曲线图、响应图和相图，受迫振动的幅频曲线和相频曲线及响应图和相图；对薄板在四种不同边界条件下的曲线图进行了比较，讨论了板厚、速度、磁感应强度及边界条件变化对薄板振动特性的影响。最后，针对轴向变速运动薄板的参数振动特性进行了分析。通过变化速度推导出了马蒂厄方程并利用平均法进行求解，得到了横向磁场中薄板振动的近似稳定性图，讨论了电磁和机械参数对薄板振动特性的影响，并对四种不同边界条件下的曲线图进行了分析比较。更多还原

【Abstract】 With the rapid development of modern science and technology, using ferromagneticconductor, piezoelectric and other materials as a major component of the electromagneticdevices has widely used in various construction projects, which makes the magneto-elasticvibration problems become increasingly apparent. With the development of electro-magnetic solid mechanics, the axial system under the action of Electromagnetic andmechanical has more and more applications to the project construction. Therefore, it isNecessary to carry out further research in this area, how to perform the safety design andreliability assessment of many vibrations in the electromagnetic environment hasimportant theoretical and practical significance.This paper mainly focuses on the axial movement of the magneto-elastic rectangularplate vibration problems under different boundary conditions. Firstly, electromagneticforce and electromagnetic torque were derived from the electromagnetic theory andMaxwell’s equations, a transverse magnetic field in the axial movement of the rectangularthin plate vibration equationwas obtained using Hamilton’s principle according to the thinplate theory and the axial movement of the motion of the system parameters.Secondly, for four different boundary conditions,we set the displacement function,and apply plus Galerkinmethod for integral equations of the system vibration. Furthermore,we derive the differential equations of free vibration, forced vibration and parametricvibration in axial motion systems. Discussed the thickness, velocity and magnetic fluxdensity change the vibration characteristics of the system.Finally, through calculating by matlab programming, axial movement of thetransverse magnetic field in the system vibration characteristics were analyzed. In the caseof given parameters, the system free vibration frequency plot,response plans and phasediagram of the forced vibration amplitude-frequency curves, phase-frequency curves andparametric vibration stability diagram were formed, diagramwereformed, By changing theparameters, the influence of electromagnetic mechanical parameters on the vibration characteristics of the systemwas was discussed, and the graph was analyzed and comparedunder four different boundary conditions.更多还原