A controllable anti-P-pseudo-Hermitian mechanical system and its application

Abstract

A novel anti-P-pseudo-Hermitian mechanical system that integrates piezoelectric actuators and sensors with non-reciprocal coupling into mechanical beams is proposed. This configuration enables the system to exhibit programmable exceptional points (EPs), which are critical for enhancing sensitivity in sensing applications. Our theoretical analysis, supported by numerical simulations and experimental validation, demonstrates the system's capability to detect minute mass variations and identify surface cracks with high precision. This advancement not only contributes to the field of non-Hermitian physics but also paves the way for the development of next-generation mechanical sensors leveraging EP physics.

Figures (5)

• Figure 1: Design of a controllable anti-P-pseudo-Hermitian system. (a) The physical illustration of the system consisting of two cantilever beams connected through piezoelectric sensors and actuators controlled by two transfer functions, $H_1$ and $H_2$, to realize non-reciprocal coupling, (b) the equivalent mass-spring model with nonreciprocal coupling.
• Figure 2: The EPs for the vibration of the anti-P-pseudo-Hermitian mechanical system. The real parts (a,c) and the imaginary parts (b,d) of the eigenfrequencies of the system with the transfer function. (a,b) and (c,d) show the results for the first- and fourth-order flexual vibration modes, respectively.
• Figure 3: Experimental demonstration of the EPs in the anti-P-pseudo-Hermitian mechanical system. (a) Schematic of experiment setup. (b) Experimental proof of the EPs for the fourth-order bending mode. (c-e) Frequency spectrum of $V_{a1}$, $V_{a2}$ and their arithmetic mean $(V_{a1}+V_{a2})/2$ for several representative values of $H$ near the fourth-order eigenfrequency. Each output voltage was independently normalized by its maximum value.
• Figure 4: Controllability of EPs for the non-Hermitian mechanical system. The programming of the transfer function ensures the exceptional point (EP) of the system following the mass perturbation (a, c) and the stiffness perturbation (b, d). (a,c) correspond to the first-order mode and (b,d) correspond to the fourth-order mode. The inserted figures show the system can be adapted to approach the EP by changing $H$ after adding a mass on beam 1 (a, c) or reducing the stiffness of beam 1 (b, d).
• Figure 5: Analysis of sensitivity of the anti-P-pseudo-Hermitian system for mechanical sensing. (a) The illustration of the system loaded by a mass and the corresponding frequency-output curves for the mass increment of $1\%$. (b) The comparison of the sensitivities of the proposed system with the conventional impedance method for mass sensing. (c) The variation of the sensitivity of the proposed system with the increase of mass perturbation. (d) The illustration of the beam with a slender surface crack and the corresponding frequency-output curve for the crack extension of $1\%$. (e) The comparison of the sensitivities of the proposed approach with the conventional impedance method for the crack growth sensing. (f) The variation of the sensitivity of the proposed approach with the increase of crack extension.