旋转运动导电圆板磁弹性振动分析  

Forced oscillation of conductive rotating circular plate in magnetic field

作　　者：李哲[1,2] 胡宇达[1,2] 姚臻臻[1,2] 

机构地区：[1]燕山大学建筑工程与力学学院,河北秦皇岛066004 [2]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,河北秦皇岛066004

出　　处：《燕山大学学报》2015年第5期464-470,共7页Journal of Yanshan University

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重点项目(ZD20131055)

摘　　要：研究了磁场中旋转运动导电薄板在外激励作用下的强迫振动问题。在给出动能、应变能和电磁能表达式的基础上,根据哈密顿原理导出旋转圆板在磁场中横向载荷作用下的轴对称磁弹性振动方程。假设位移函数并运用分离变量法分离时间变量和空间变量,应用伽辽金积分法,得到激励作用下圆板的强迫振动微分方程并求解。通过数值计算得到简支和固支两种边界条件下的幅频曲线和相轨迹图,分析磁感应强度、圆板的厚度、半径和转速的变化对振动的影响。Forced oscillation of a conductive rotation thin circular plate under external excitation in magnetic field is investigated. By using Hamilton principle,the magneto-elastic vibration equations of a conductive rotating thin circular plate are deduced under the action of transverse load with the expressions of kinetic energy and strain energy considered. According to the set of a displacement function and the separation of time and spatial variables with the method of separation of variables,forced oscillation differential equation with the load is obtained and solved through the application of Galerkin integral method. The amplitude-frequency and phase trajectory curves are obtained with fixed and simply supported boundary condition through the numerical calculation,the stability. The influence of magnetic induction intensity,rotation speed,plate thickness and radius on the vibration of the spinning plate are analyzed finally.

关 键 词：磁弹性 旋转圆板 振动 轴对称 伽辽金法 

分 类 号：O442[理学—电磁学] O327[理学—物理]