Modal damping ratios of the two-degree-of-freedom acoustic model having a Helmholtz resonator

Helmholtz resonators are used in many industrial products as devices for reducing low-frequency noise. An advantage of the Helmholtz resonator is that the structure is simple and applicable to low-frequency noise for its size. Further, an important feature is that the development costs and product costs are relatively low in actual product development. The optimum combination of the natural frequency and modal damping ratio of a Helmholtz resonator is dependent on the characteristic of the noise source. It is selected so as to minimize the sound pressure levels when the noise is stationary. In the case of a transient noise problem, the natural frequency and modal damping ratio is tuned for maximizing the modal damping ratios of the system consisting of the main system and a Helmholtz resonator. Noise reduction effects of Helmholtz resonators are generally predicted by 3D acoustic analysis. Recently, the effects are estimated by CFD at higher sound pressure levels exceeding 100dB, because they are greatly affected by eddies generated in the neck portion of resonators. However, there is no suitable method to predict the noise reduction effects of Helmholtz resonators that engineers can use easily in the early stages of design. This paper describes a simple method for estimating the optimum value of modal damping ratios of the acoustic system having a Helmholtz resonator. Here, two-degrees-of-freedom models similar to the mass-spring-damper models used in the design of tuned mass dampers are used. In addition, the differences between the optimum conditions of tuned mass dampers and Helmholtz resonators are described.