Low-frequency sound insulation performance of novel membrane acoustic metamaterial with dynamic negative stiffness

Abstract

For improving the low-frequency sound insulation properties of membrane/plate structures, a new quasi-zero stiffness membrane acoustic metamaterial with dynamic magnetic negative stiffness is proposed. Upon applying the equivalent magnetic charge theory to derive the dynamic magnetic negative stiffness, a theoretical model of proposed metamaterial with finite dimensions is established based on the Galerkin method. Through a combination of theoretical analysis, numerical simulation and experimental measurement, the low-frequency (1—1000 Hz) sound insulation performance of the metamaterial is investigated from several perspectives, including structural modality, vibration mode, average velocity, phase curve, equivalent mass density, and equivalent spring-mass dynamics model. Results show that, at a certain initial membrane tension, decreasing the magnetic gap or increasing the residual flux density can increase the dynamic magnetic negative stiffness. This in turn leads to decreased peak frequency and enlarged bandwidth of sound insulation, thus achieving effective low-frequency sound insulation over a wide frequency band. Further, when the magnetic gap is larger than the second critical magnetic gap and smaller than the first critical magnetic gap, the first-order modal resonance of the metamaterial disappears, and the corresponding value of sound insulation valley increases significantly, thus demonstrating superior sound insulation effect with wide frequency band. The proposed method of using dynamic magnetic negative stiffness to improve low-frequency sound insulation valleys due to modal resonance provides useful theoretical guidance for designing membrane/plate type low-frequency sound insulation metamaterials.