Optimum tuning of damped side-branch silencer using equivalent discrete model and considering open-end correction

Abstract

This paper describes the optimum tuning of damped side-branch silencers. As is well known, a side-branch silencer is a type of vibration absorber; however, damped side-branch silencers have not yet been sufficiently studied. In this study, to derive the optimum tuning conditions of a side-branch silencer, modal analysis was applied to wave equations of a host acoustic field and a side-branch silencer. Using the equations of motion with the modal coordinate system, an equivalent discrete model of the coupled vibration system between the host acoustic field and side-branch silencer was obtained. The degrees of freedom of the equivalent discrete model were reduced to two by ignoring the non-related acoustic modes, and the two fixed point method was applied to the two degree of freedom vibration system to derive the optimum natural frequency ratio and optimum loss factor of the side-branch silencer. In addition, open-end correction of the side-branch silencer was formulated considering the effect of residual acoustic modes of the host acoustic field. A theoretical analysis with respect to the optimum tuning conditions and open-end correction was validated through simulations and experiments.

Keywords

• side-branch
• silencer
• dynamic vibration absorber
• acoustic field
• modal analysis
• open-end correction
• residual modes
• damping