Optimum tuning of damped Helmholtz silencer using an equivalent discrete model and considering open-end correction

This paper describes the optimum tuning of damped Helmholtz silencers. In this study, Helmholtz resonators are used as silencers that suppress acoustic resonance in host acoustic fields. Side branch silencers and Helmholtz silencers are commonly known as a type of vibration absorber; however, damped silencers have not been thoroughly studied thus far. Therefore, prior to this paper, we reported the optimum tuning of damped side branch silencers using modal analysis and two fixed point method. In this paper, we additionally describe the optimum tuning of damped Helmholtz silencers in a similar fashion as in our previous paper. The resonance mechanism of Helmholtz silencers is different from that of side branch silencers. The coupled vibration between the host acoustic field and Helmholtz silencer was theoretically analyzed using modal analysis in this study. An equivalent discrete model was obtained using the equations of motion using modal coordinate systems. Using the equivalent discrete model, the open-end correction of the neck of the Helmholtz silencer was considered, and the number of degrees of freedom of the equivalent discrete model was reduced to two to derive optimum tuning conditions using the two fixed point method. The optimum natural frequency ratio and loss factor of the Helmholtz silencer were derived using the vibration model with two degrees of freedom. The theoretical analysis was validated through simulations and experiments.