Nonlinear vibration characteristics and noise reduction performance of honeycomb metamaterial structures with hysteretic nonlinearity

Vibration and noise are key factors affecting the technical performance of modern equipment. With the trend toward smarter and more compact marine exploration equipment, there is an urgent need for ultra-thin, lightweight, and pressure-resistant underwater acoustic metamaterials. In this paper, a honeycomb acoustic metamaterial embedded with a hysteretic nonlinear resonator is proposed. Based on the improved Van der Pol method, the dynamic equations of the honeycomb metamaterial with hysteretic nonlinear characteristics are established. Based on the harmonic balancing method, the influence of hysteresis parameters on vibration characteristics and stability characteristics is analyzed under simple harmonic acoustic excitation. Then, the effects of nonlinear parameters on the characteristics of stochastic vibrations are discussed using the maximum Lyapunov exponent and the steady-state probability density function. Finally, the impact of structural dimensional parameters on noise reduction performance is investigated. Three different types of nonlinear resonators are proposed to achieve low-frequency bandgap tuning, and their underwater noise reduction performance is discussed. This study provides a reference for the design of lightweight and thin-walled honeycomb acoustic metamaterial structures, promotes their application in underwater noise reduction, and holds significant academic value and application potential.