摘要
通过建立磁场中铁磁矩形板的力学模型,对其在常磁场下的非线性固有振动问题进行研究,并分析静载效应。根据哈密顿变分原理,得到磁场中铁磁矩形板的磁弹性非线性振动方程,给出磁化电磁力和涡流电磁力表达式。基于摄动展开法,确定静磁力作用下的静挠度和非线性扰动方程。应用伽辽金法与多尺度法,得出振动系统近似解析解和固有频率表达式。通过算例,给出了3种材料的矩形薄板固有频率随时间、磁场强度、初值、边长比等的变化规律特性曲线图。结果表明:固有频率随时间的增大,最终会趋于一定值,随上下表面磁场的变化,会呈现出对称的趋势,随边长比的增大,其频率会逐渐减小;系统呈现典型的非线性特征,解析解与数值解较为吻合。
Here, through establishing mechanical model of ferromagnetic rectangular plate in magnetic field, its nonlinear natural vibration in constant magnetic field was studied, and static load effect was analyzed.According to Hamilton variational principle, the magnetoelastic nonlinear vibration equation of ferromagnetic rectangular plate in magnetic field was derived to obtain expressions for magnetizing electromagnetic force and eddy current electromagnetic force. Based on the perturbation expansion method, static deflection and nonlinear perturbation equations of plate under the action of static magnetic force were determined.Using Galerkin method and multi-scale method, the approximate analytical solution and natural frequency expression of vibration system were obtained. Characteristic curves of natural frequencies of rectangular thin plates made by 3 kinds of materials versus time, magnetic field intensity, initial value and side length ratio were given with examples. The results showed that with increase in time, each natural frequency can eventually tend to a certain value;with change of magnetic fields on upper and lower plate surfaces, natural frequencies can reveal symmetrical trend;with increase in side length ratio, natural frequencies can gradually decrease;vibration system presents typical nonlinear characteristics, its analytical solution agrees better with its numerical solution.
作者
陶善泽
胡宇达
TAO Shanze;HU Yuda(School of Civil Engineering and Mechanics,Yanshan University,Qinhuangdao 066004,China;Hebei Key Laboratory of Mechanical Reliability for Heavy Equipment and Large Structures,Yanshan University,Qinhuangdao 066004,China)
出处
《振动与冲击》
EI
CSCD
北大核心
2023年第3期74-82,共9页
Journal of Vibration and Shock
基金
国家自然科学基金(12172321,11472239)
河北省自然科学基金(A2020203007)。
关键词
铁磁矩形板
非线性固有振动
常磁场
静载效应
多尺度法
ferromagnetic rectangular plate
nonlinear natural vibration
constant magnetic field
static load effect
multi-scale method
