NONLINEAR VIBRATION CONTROL OF DISCRETE DYNAMICS SYSTEMS BASED ON NON-HERMITIAN SKIN EFFECT

Nonlinear dynamical systems exhibit large wavelengths, broad frequency bands, and a significant degree of nonlinearity in their low-frequency broadband vibration response. Scientific challenges such as dimensional constraints, harmonic frequencies, multi-frequency components, and full-band vibration control have been long-standing technical issues that remain unresolved. This paper presents a multi-degree-of-freedom nonlinear spring-mass system, wherein a discrete non-Hermitian system exhibiting a skin effect is created with the application of independently adjustable unidirectional forces. The nonlinear dispersion relationship within the complex domain of the system is examined using perturbation methods. This elucidates nonreciprocal wave transmission properties, energy confinement zones and modes of nonlinear oscillations, as well as the influence of the skin effect on nonlinear vibrational responses. The results show that the unidirectional force breaks the symmetry of the dispersion relation, leading to nonreciprocal wave transmission that propagates in only one direction. In this case, the vibration energy is localized to a specific direction, and the skin effect is apparent. The design of non-Hermitian systems enables low-frequency broadband vibration control in linear spring-mass systems and across weak, intermediate and strong nonlinearities. Additionally, it can be used to regulate and switch vibration modes, including periodic limit cycles, quasi-periodic vibrations, and chaotic vibrations. The non-Hermitian system design methodology presented in this article provides insights for low-frequency broadband vibration control and the modulation of vibration modes in complex nonlinear dynamical systems, offering a possibility for broadband control applications.