We investigate non-Hermitian degeneracies, also known as exceptional points, in continuous 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. The introduction of external perturbations leads to a splitting of the eigenvalues, which is explored as a sensitive approach to the 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 analyses. 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.

我们研究连续弹性介质中的非Hermitian退化，也称为例外点，及其在质量和刚度扰动检测中的潜在应用。退化状态是通过通过量身定制的平衡增益和损耗强制执行奇偶校验时间对称性而引入的，并以复数刚度的形式引入，并且可以通过压电换能器实现。外部扰动的引入导致特征值的分裂，这被探索为检测这种扰动的灵敏方法。一维波导的数值模拟说明了其振动谱中存在多个异常点，并从概念上证明了其对点质量包含物的敏感性。示出了二阶例外点在频谱中表现出频移，其平方根依赖于被扰动质量，这被扰动方法和频率响应分析所证实。然后研究了支持导波的弹性域，其中通过兰姆波模式的混合形成了特殊的点。在说明了对点质量夹杂物的类似敏感性之后，我们还展示了如何将这些概念应用于表面波模式以检测裂纹类型的缺陷。提出的结果描述了支持特殊点的PT对称弹性介质的基本振动特性，其对扰动的敏感性超出了Hermitian系统中通常遇到的线性依赖性。