Realization of Higher-Order Exceptional Points in Anti-P-Pseudo-Hermitian Mechanical System

Anti-P-pseudo-Hermitian (APPH) systems have recently emerged as a promising frontier in controllable non-Hermitian physics, enabling spectral degeneracies solely through coupling constraints—without the balanced gain–loss requirement of parity-time (PT )-symmetric systems. However, translating this concept to mechanical platforms remains challenging, particularly for higher-order systems that demand multiple coupling constraints, due to the difficulty of realizing practical nonreciprocal coupling. Here, we present a general, fabrication-friendly mechanical system for implementing high-order APPH dynamics by integrating a piezoelectric sensor–actuator-feedback control. We develop a theoretical framework that maps the continuous mechanical platform to an equivalent coupled-mode model, illustrating how tailored coupling control allows flexible realization of high-order exceptional points (EPs). Under micromass perturbations, the system simultaneously exhibits second-order and third-order frequency splitting behaviors, achieving enhanced sensitivity and significantly extending the sensing range beyond that of a single EP. Numerical simulations validate both the feasibility of the proposed design and its superior sensing performance. This work establishes a versatile approach for engineering higher-order non-Hermitian symmetries in mechanical systems, offering not only improved sensing capabilities but also a robust platform for exploring a wide range of non-Hermitian phenomena.