Exceptional points for crack detection in non-Hermitian beams

Abstract

We study exceptional points (EPs) in parity-time (PT) symmetric non-Hermitian beams and explore their applications in crack detection. The EPs are formed by coupling different beam modes under feedback-controlled forces. The variations of the required non-Hermitian coefficient for the achievement of EPs are studied as a function of the separations and center positions of the applied force pairs. Then, a 3D cuboid-shaped crack is introduced at the center of the top surface of the beam, and results in the square-root behaviors of the frequency splitting under different crack geometries and force polarizations. This supports the enhanced sensitivity based on EPs as compared to the usual linear sensing methods. Using several polarizations allows access to different types of waves propagating in the beam and their modifications in the presence of the crack, therefore providing combined means of testing. Furthermore, a practical and feasible feedback control design is realized via replacing the applied forces by piezoelectric patches on the beam surface, exhibiting highly sensitive responses of the EPs to minor cracks. The studied results provide a new platform for crack or perturbation detection in elastic media.