带质量梁的Eigenvalue分布
On the Eigenvalue Distribution for a Beam with Attached Masses
摘要：
本文研究了一种由压电作动器和电磁振动台组成的铰接柔性梁的数学模型。振动筛被建模为一个质量和弹簧系统连接到梁。为了分析这个机械系统的自由振动，我们考虑了相应的频谱问题的四阶微分算子的交界条件，表征振动台的动态。对特征方程进行了解析研究，得到了特征值的渐近估计。本征值分布也说明了数值模拟下的一个现实的选择的机械参数。
英文摘要：
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.
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