Tuning a semi-active Helmholtz resonator S. Singh a , C. Q. Howard b , C. H. Hansen c School of Mechanical Engineering The University of Adelaide Adelaide, S.A. Australia, 5005 ABSTRACT Adaptive Helmholtz resonators are used to reduce tonal noise propagating as plane waves in ducts. Optimal tuning of the resonator has previously been achieved by using a pressure sensor located in the duct downstream of the resonator. The work described here is concerned with the development of a cost function that could be used by a con- troller to optimally tune the Helmholtz resonator without any in-duct pressure sensor. The cost function that was developed is based on the phase difference between the pressure at the top of the closed end of the cavity of the Helmholtz resonator and the pressure at the neck wall, close to the neck duct interface. Damping in the system is taken into account using a correction factor applied to the cost function. 1 INTRODUCTION 1.1 Motivation The problem of low-frequency tonal noise is inherent in industries using internal com- bustion (IC) engines, compressors, fans, blowers, power transformers, gearboxes etc. The humming nature of a tonal noise not only causes annoyance to workers within the industry but also to the surrounding community. Depending upon the type of application, existing set up and cost constraints, tonal noise transmission can be controlled in many possible ways like by installing reactive silencers, barriers, side branch elements and active noise control devices. The work described here is concerned with the attenuation of tonal noise transmission in ducts by using side branch resonators. Passive Helmholtz resonators (HRs) are specifically designed to achieve their optimal performance at one frequency only, and are only effective over a very narrow frequency band. Any slight change in the frequency, change in temperature which changes the speed of sound and hence the wavelength of the noise will decrease the effectiveness of the resonator. Resonators incorporating the provision for altering their geometrical parame- ters in real-time in order to adapt themselves to the environmental or operating condition changes offer an obvious solution. Such an adaptive system is referred to as a semi-active system in which a change in the physical parameters of the passive element is caused by an active control system. Because of the benefits of semi-active systems over any ex- clusive active and passive systems [1, 2], semi-active systems are gaining popularity in industry. Some of the industrial applications of the semi-active systems are highlighted in the next section. a Email address: sarabjeet.singh@adelaide.edu.au b Email address: carl.howard@adelaide.edu.au c Email address: colin.hansen@adelaide.edu.au