PT对称连续弹性介质中的例外点与灵敏度增强
Exceptional points and enhanced sensitivity in PT-symmetric continuous elastic media
摘要：
我们调查非厄米退化，也被称为例外点，在连续弹性介质中，和它们的潜在应用检测的质量和刚度扰动。简并状态是通过定制的平衡增益和损耗来强制奇偶时间对称性而引起的，以复刚度的形式引入，并且可以通过压电式传感器来实现。由外部扰动引起的这种对称性的破坏会导致本征值的分裂，这被探索为检测此类扰动的一种敏感方法。一维波导的数值模拟说明了几个例外点在其振动谱的存在下，并从概念上证明了其灵敏度的质点夹杂物。二阶例外点示出表现出的频谱中的频率偏移的平方根依赖于扰动的质量，这是确认的扰动方法和频率响应预测。支持导波的弹性域，然后调查，其中例外点形成的杂交兰姆波模式。在说明了类似的灵敏度质点夹杂物，我们还展示了如何将这些概念可以应用到表面波模式感测裂纹型缺陷。所提出的结果描述的基本振动特性的PT-对称弹性介质支持例外点，其扰动的敏感性超出了通常遇到的线性依赖厄米特系统。因此，研究结果是有前途的应用，涉及传感的扰动，如增加的质量，刚度不连续性和表面裂纹。
英文摘要：
We investigate non-Hermitian degeneracies, also known as exceptional points, in continous elastic media, and their potential application to the detection of mass and stiffness perturbations. Degenerate states are induced by enforcing parity-time symmetry through tailored balanced gain and loss, introduced in the form of complex stiffnesses and may be implemented through piezoelectric transducers. Breaking of this symmetry caused by external perturbations leads to a splitting of the eigenvalues, which is explored as a sentitive approach to detection of such perturbations. Numerical simulations on one-dimensional waveguides illustrate the presence of several exceptional points in their vibrational spectrum, and conceptually demonstrate their sensitivity to point mass inclusions. Second order exceptional points are shown to exhibit a frequency shift in the spectrum with a square root dependence on the perturbed mass, which is confirmed by a perturbation approach and by frequency response predictions. Elastic domains supporting guided waves are then investigated, where exceptional points are formed by the hybridization of Lamb wave modes. After illustrating a similar sensitivity to point mass inclusions, we also show how these concepts can be applied to surface wave modes for sensing crack-type defects. The presented results describe fundamental vibrational properties of PT-symmetric elastic media supporting exceptional points, whose sensitivity to perturbations goes beyond the linear dependency commonly encountered in Hermitian systems. The findings are thus promising for applications involving sensing of perturbations such as added masses, stiffness discontinuities and surface cracks.
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