弱各向异性柔性转子的Campbell图
Campbell diagrams of weakly anisotropic flexible rotors
摘要：
我们考虑一个轴对称的转子扰动耗散，保守和非保守的位置力起源于与各向异性定子接触。未扰动系统的坎贝尔图在频率-速度平面上是一个网状结构，在节点处具有双本征频率。该图便于分析旋转弹性连续体中的行波。计算灵敏度的双峰，我们发现，在每一个特定的节点的解扭的网格到分支的复杂的特征值在第一近似一般由四个2 × 2的子块的扰动矩阵。在亚临界速度范围内引起自激振动的不稳定模式的选择受奇异本征值表面拐角处的例外点--“双咖啡过滤器”和“高架桥”--的支配，这些点与具有明确Krein签名的未扰动坎贝尔图的交叉点有关。奇异性将波在旋转连续介质中的传播问题与电磁波和声波在非旋转各向异性手征介质中的传播问题联系起来。作为力学实例，详细研究了两个自由度的旋转轴模型和旋转圆弦穿过圆柱体的连续模型。
英文摘要：
We consider an axi-symmetric rotor perturbed by dissipative, conservative, and non-conservative positional forces originated at the contact with the anisotropic stator. The Campbell diagram of the unperturbed system is a mesh-like structure in the frequency-speed plane with double eigenfrequencies at the nodes. The diagram is convenient for the analysis of the traveling waves in the rotating elastic continuum. Computing sensitivities of the doublets we find that at every particular node the untwisting of the mesh into the branches of complex eigenvalues in the first approximation is generically determined by only four 2x2 sub-blocks of the perturbing matrix. Selection of the unstable modes that cause self-excited vibrations in the subcritical speed range, is governed by the exceptional points at the corners of the singular eigenvalue surfaces--`double coffee filter' and `viaduct'--which are associated with the crossings of the unperturbed Campbell diagram with the definite Krein signature. The singularities connect the problems of wave propagation in the rotating continua with that of electromagnetic and acoustic wave propagation in non-rotating anisotropic chiral media. As mechanical examples a model of a rotating shaft with two degrees of freedom and a continuous model of a rotating circular string passing through the eyelet are studied in detail.
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