论文标题
在具有附着质量的光束的特征值分布上
On the Eigenvalue Distribution for a Beam with Attached Masses
论文作者
论文摘要
我们在本文中研究了带有压电执行器和电磁振荡器的铰链柔性光束的数学模型。振动筛被建模为附着在光束上的质量和弹簧系统。为了分析该机械系统的自由振动，我们考虑了具有表征振动摇动力学的界面条件的四阶差分操作员的相应光谱问题。分析研究了特征方程，并获得了特征值的渐近估计。在机械参数的现实选择下，数值模拟还可以说明特征值分布。
We study a mathematical model of a hinged flexible beam with piezoelectric actuators and electromagnetic shaker in this paper. The shaker is modelled as a mass and spring system attached to the beam. To analyze free vibrations of this mechanical system, we consider the corresponding spectral problem for a fourth-order differential operator with interface conditions that characterize the shaker dynamics. The characteristic equation is studied analytically, and asymptotic estimates of eigenvalues are obtained. The eigenvalue distribution is also illustrated by numerical simulations under a realistic choice of mechanical parameters.
