Exceptional Points and Skin Modes in Non-Hermitian Metabeams

Abstract

We present a non-Hermitian metabeam exhibiting an exceptional point (EP) induced by enforcing parity-time (PT) symmetry through applied external forces. The EP is formed by the hybridization of two flexural wave modes and its output displacement is enhanced by attaching two pillars on top of the beam. The introduction of a tiny mass perturbation that breaks the PT symmetry leads to a splitting of the eigenfrequencies at the EP with a square-root dependence on the perturbation mass. This effect manifests itself in a splitting of resonant peaks in the frequency response. The enhanced sensitivity of the EP paves the way to the detection of small perturbations such as tiny masses and cracks. Another property of the metabeam is the existence of skin modes whose energies are localized at one end of the beam and can be generated by implementing nonreciprocal feedback interactions between the pillars. We demonstrate that the skin modes are broadband and independent of the excitation positions. From a practical perspective, we show the great potential of skin modes in broadband energy harvesting. Our study proposes approaches to manipulate the non-Hermitian elastic wave phenomena, paving the way for the development of highly sensitive sensors, vibration control, and energy harvesting.

Non-local and non-Hermitian acoustic metasurfaces

“…In general, a PT -symmetric 1D system features an asymmetric response from opposite sides, and such asymmetric behavior reaches an extreme at the EP, where unidirectional transparency or unidirectional reflectionlessness can be observed [104,108,150]. Beyond EPs, in the PT -broken phase, all bulk modes can be localized at a given boundary, which is known as the non-Hermitian skin effects (NHSEs) derived from the unconventional bulk-boundary correspondence in non-Hermitian systems [114,118,[151][152][153][154][155]. As will be discussed in section 4.6, NHSE is another important feature of the non-Hermitian system.…”

“…On the other hand, the ultra-high sensitivity of a system at EP essentially amplifies any small parametric variations, a useful property for sensor applications [167]. It has been shown that a non-Hermitian system operating in close vicinity of an EP, with the eigenfrequencies of the relevant non-Hermitian modes being highly sensitive to perturbations to the system [117,118,126,168], has potential applications in ultrasonic inspection, noise detection, and vibration accelerometer. Moreover, unidirectional transparency stemming from non-Hermitian acoustic systems can also be utilized to realize an acoustic directional cloak [104,110].…”

“…One of the most common solutions is to utilize loudspeakers with elaborately designed feedback circuits to artificially amplify the acoustic signal [108][109][110][111]. Another common approach is to induce feed-back controlled piezoelectric elements (PZT for example) based on the electromechanical coupling effect [112][113][114][115][116][117][118], which is more practical for manipulating elastic waves where speaker are not suitable [113,114,[116][117][118][119]. Besides these active sound generating units with feedback control, acoustic gain can also be realized by leveraging flowinduced sound [120], based on the hydrodynamic instability theory.…”

Non-Hermitian acoustic waveguides with periodic electroacoustic feedback

“…Although all topological aspects of the NHSE -in contrast with Hermitian topological modes -can be studied in simpler single-band periodic systems with one degree of freedom per unit cell, distributed-parameter models with an infinite number of bands in the reciprocal space are more realistic in representing practical applications. This work makes contributions in this direction, using acoustic one-dimensional waveguides with periodically applied electroacoustic feedback, following a design strategy that emulates both nearest-neighborhood and long-range non-reciprocal coupling by applying local and non-local feedback interactions, respectively [24,25,30,20].…”

“…These systems may find a myriad of applications in engineering, wherever mechanical waves need to be localized and filtered. For instance, investigations suggest that they can be used as design strategies to control filaments and membranes in biological systems [20] and may also be highly effective for broad-band energy harvesting, when compared to traditional approaches [30].…”