Stability of a flexible structure with destabilizing boundary conditions
Stability of a flexible structure with destabilizing boundary conditions
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具有不稳定边界条件的柔性结构的稳定性
DOI：
10.1098/rspa.2016.0109
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
V. Shubov
中科院分区：
文献类型：
--
作者：
M. Shubov;V. Shubov
研究了具有反馈控制型非耗散边界条件的Euler-Bernoulli梁模型。二维输入矢量的分量是右端的剪力和力矩，观测矢量的分量是右端的位移和斜率的时间导数。依赖于两个控制参数的共对角矩阵将输入和观测联系起来。本文有五个结果。首先，本征模的渐近近似推导。二是确立了“主体身份”。它提供了两个系统的模态之间的关系：一个具有非零控制参数，另一个具有零控制参数。第三，当一个控制参数为正，另一个为零，“主恒等式”产生的所有本征模的稳定性（虽然系统是非耗散的）。第四，将本征模的稳定性推广到一个控制参数为正，另一个控制参数足够小的情况。最后，研究了无差拍模式的存在性和性质。
The Euler–Bernoulli beam model with non-dissipative boundary conditions of feedback control type is investigated. Components of the two-dimensional input vector are shear and moment at the right end, and components of the observation vector are time derivatives of displacement and slope at the right end. The codiagonal matrix depending on two control parameters relates input and observation. The paper contains five results. First, asymptotic approximation for eigenmodes is derived. Second, ‘the main identity’ is established. It provides a relation between mode shapes of two systems: one with non-zero control parameters and the other one with zero control parameters. Third, when one control parameter is positive and the other one is zero, ‘the main identity’ yields stability of all eigenmodes (though the system is non-dissipative). Fourth, the stability of eigenmodes is extended to the case when one control parameter is positive, and the other one is sufficiently small. Finally, existence and properties of ‘deadbeat’ modes are investigated.