Exceptional Points Induced by Time-Varying Mass to Enhance the Sensitivity of Defect Detection

The exceptional point (EP), a non-Hermitian degeneracy at which eigenvalues and eigenvectors coalesce simultaneously, is investigated in mechanical oscillators involving a time-varying mass. A dynamic modulation mechanism is employed to create the time-varying mass, which can potentially develop an EP by acting as an energy source and drain. To fully demonstrate the existence of EPs, the eigenvalue problem for the modulated system is theoretically formulated through two different schemes, based on the state-space and harmonic balance methods. A second-order EP is confirmed by both methods and exists as a result of the coalescence of fundamental and harmonic eigenmodes. As a salient property of this second-order EP, the square-root behavior of the eigenfrequency subject to small perturbations of the system parameters is theoretically demonstrated, and utilized to devise a proof-of-concept model for mechanical sensors with high sensitivity to void defects in elastic solids. The EP behavior induced by a time-varying mass may find potential applications in damage assessment and health monitoring of engineering structures.