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首页> 外文期刊>International journal of structural stability and dynamics >Eigenanalyses of Functionally Graded Micro-Scale Beams Entrapped in an Axially-Directed Magnetic Field with Elastic Restraints
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Eigenanalyses of Functionally Graded Micro-Scale Beams Entrapped in an Axially-Directed Magnetic Field with Elastic Restraints

机译：带有弹性约束的轴向磁场中截留的功能梯度微尺度梁的本征分析

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摘要

Approximate numerical solutions are obtained for the vibration response of a functionally graded (FG) micro-scale beam entrapped within an axially-directed magnetic field using the differential transformation method (DTM). Idealized as a one-dimensional (1D) continuum with a noticeable microstructural effect and a thickness-directed material gradient, the microbeam's behavior is studied under a range of nonclassical boundary conditions. The immanent microstructural effect of the micro-scale beam is accounted for through the modified couple stress theory (MCST), while the microscopic inhomogeneity is smoothened with the classical rule of mixture. The study demonstrates the robustness and flexibility of the DTM in providing benchmark results pertaining to the free vibration behavior of the FG microbeams under the following boundary conditions: (a) Clamped-tip mass; (b) clamped-elastic support (transverse spring); (c) pinned-elastic support (transverse spring); (d) clamped-tip mass-elastic support (transverse spring); (e) clamped-elastically supported (rotational and transverse springs); and (f) fully elastically restrained (transverse and rotational springs on both boundaries). The analyses revealed the possibility of using functional gradation to adjust the shrinking of the resonant frequency to zero (rigid-body motion) as the mass ratio tends to infinity. The magnetic field is noted to have a negligibly minimal influence when the gradient index is lower, but a notably dominant effect when it is higher.
机译：使用微分变换方法（DTM）获得了截留在轴向磁场中的功能梯度（FG）微型光束的振动响应的近似数值解。理想化为具有明显微结构效果和厚度方向的材料梯度的一维（1D）连续体，在一定范围的非经典边界条件下研究了微束的行为。微观梁的内在微观结构效应是通过改进的耦合应力理论（MCST）解决的，而微观不均匀性则通过经典的混合规则得以平滑。这项研究证明了DTM在提供与FG微束在以下边界条件下的自由振动行为有关的基准结果方面的鲁棒性和灵活性：（a）夹头质量; （b）夹紧弹性支撑（横向弹簧）; （c）销钉弹性支撑（横向弹簧）; （d）尖端弹性弹性支撑（横向弹簧）; （e）夹紧弹性支撑（旋转弹簧和横向弹簧）; （f）完全受到弹性约束（两个边界上的横向和旋转弹簧）。分析表明，随着质量比趋于无穷大，可以使用功能渐变将共振频率的收缩率调整为零（刚体运动）。注意到当梯度指数较低时，磁场的影响微乎其微，而当梯度指数较高时，磁场的显着支配作用。

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