Advances in vibration and wave modulation of non-Hermitian dynamic systems

The band characteristics of periodic structures offer effective methods for controlling vibrations and waves. Traditional designs of periodic structures for vibration and wave control primarily rely on passive, non-interactive materials, which inherently belong to Hermitian systems. These systems adhere to energy conservation laws, limiting the range of vibration and wave control capabilities. In recent years, research on non-Hermitian dynamical systems has challenged the conventional understanding of band theory. The discovery of the skin effect has provided new avenues for vibration and wave control. This effect manipulates the complex frequency domain characteristics of a system’s eigenstates, inducing elastic waves to form directional skin modes, where wave energy is localized at the boundaries of a finite system. This paper introduces the basic principles of the non-Hermitian skin effect (NHSE) and outlines the mechanisms for low-frequency broadband vibration and wave control in non-Hermitian systems. It reviews recent advances in vibration control and wave modulation, covering both discrete and continuous system design methods, control mechanisms, and implementation strategies. The paper also discusses key challenges in the field and explores potential future directions for research.Non-Hermitian systems, in contrast to traditional Hermitian systems, allow for energy exchange with the external environment. As a result, their band structures extend into the complex plane, where the imaginary part represents asymmetric gain or loss. This introduces directional, non-reciprocal wave propagation behaviors, fundamentally different from those observed in Hermitian systems. The non-Hermitian skin effect facilitates boundary localization of waves and directional confinement of vibration energy, offering new possibilities for broad-band vibration and wave control. By designing asymmetric gain/loss profiles, non-Hermitian systems break the spatial non-locality of waves and allow for directional energy control.The directional wave propagation induced by the skin effect has been widely studied in fields such as electromagnetics and acoustics. In these areas, the energy localization properties of the non-Hermitian skin effect have been used in the design of directional waveguides, sound absorption, and noise isolation devices. These studies have led to one-way wave transmission, directional attenuation, and amplitude amplification/suppression, providing new perspectives for applications in waveguide communication and noise reduction. Despite these advances, the application of the non-Hermitian skin effect to elastic wave control remains in its early stages, with challenges such as lack of design theory, unclear control mechanisms, and difficulties in experimental validation. In light of the potential of the non-Hermitian skin effect for broadband vibration and wave control, this paper offers a detailed examination of its mechanisms and characteristics. It presents an overview of recent developments in vibration and wave control, and highlights the fundamental principles, research progress, and future challenges in this field.