Asymptotics of the eigenmodes and stability of an elastic structure with general feedback matrix
Asymptotics of the eigenmodes and stability of an elastic structure with general feedback matrix
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具有一般反馈矩阵的弹性结构的本征模态和稳定性的渐进性
DOI：
10.1093/imamat/hxz019
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发表时间：
2019
影响因子：
1.2
通讯作者：
Kindrat, Laszlo P
中科院分区：
文献类型：
--
作者：
Shubov, Marianna A;Kindrat, Laszlo P
研究了完全非耗散边界条件下Euler-Bernoulli梁的固有频率分布。梁在左端被固定，在右端被配置一个四参数（）线性边界反馈律。边界反馈矩阵将控制输入（右端的速度矢量及其空间导数）与输出（右端的剪切矢量和力矩）联系起来。描述梁动力学的初边值问题在具有能量范数的状态Hilbert空间中化为一阶时间演化方程。动力学发生器具有由表示的纯离散频谱（振动模式）。本文研究了控制参数的作用，并证明了下列结果：（i）当，振动模集渐近地接近于方程所给出的复平面上的垂线时，（ii）当，（4）当，，
The distribution of natural frequencies of the Euler–Bernoulli beam subject to fully non-dissipative boundary conditions is investigated. The beam is clamped at the left end and equipped with a 4-parameter () linear boundary feedback law at the right end. Theboundary feedback matrix relates the control input (a vector of velocity and its spatial derivative at the right end), to the output (a vector of shear and moment at the right end). The initial boundary value problem describing the dynamics of the beam has been reduced to the first order in time evolution equation in the state Hilbert space equipped with the energy norm. The dynamics generator has a purely discrete spectrum (the vibrational modes) denoted by. The role of the control parameters is examined and the following results have been proven: (i) when, the set of vibrational modes is asymptotically close to the vertical line on the complex-plane given by the equation; (ii) whenand the parameteris such thatthen the following relations are valid:andas; (iii) when,, and, then the following relations are valid:andas; (iv) when,, and, then the following relations are valid:andas.
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DOI：
10.1098/rspa.2016.0109
发表时间：
2016
期刊：
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
影响因子：
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作者：
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DOI：
10.1109/cdc.1992.371264
发表时间：
1992
期刊：
[1992] Proceedings of the 31st IEEE Conference on Decision and Control
影响因子：
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作者：
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影响因子：
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影响因子：
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作者：
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通讯作者：
W. Paulsen