《《resonant frequency of an adjustable helmholts resonator in a hydraulic system》.pdf

Arch Appl Mech (2009) 79: 1115–1125 DOI 10.1007/s00419-008-0279-5 ORIGINAL Lari Kela Resonant frequency of an adjustable Helmholtz resonator in a hydraulic system Received: 10 April 2008 / Accepted: 18 November 2008 / Published online: 16 December 2008 © Springer-Verlag 2008 Abstract An adjustable Helmholtz resonator in hydraulics is studied because of obvious lack of studies in the field. First the theory of a Helmholtz resonator is reviewed by examining older studies on the subject. Most of the previous studies have covered Helmholtz resonators in acoustics, but the same basic theory can be applied to hydraulics. After the theory review the test equipment and measurement methods are presented and some results are calculated analytically using the classical model and a modified model that takes the effect of spring mass into consideration. The spring mass is taken into account because the density of hydraulic oil is over 700 times greater than the density of air. In the last section the results of the calculations and measurements are discussed, and it is noted that the results of the experiments agree better with the modified model of classical Helmholtz theory. Some explanations for residual discrepancies are given but also some remarks are presented. Keywords Helmholtz resonator · Hydraulics · Resonance 1 Introduction The aim of the study was to learn to define the resonant frequency of a Helmholtz resonator in a hydraulic system so that it can be used as a damper of a certain frequency, cf. spring mass dampers in mechanics. A theory review was conducted in acoustics because only a few studies about Helmholtz resonators in hydraulics can be found. The theory review was supported by analytical calculation and finally, by verification measurements. Figure 1 presents a simple example of a Helmholtz resonator and a single-degree-of-freedom system that is analogous to a Helmholtz resonator. A Helmholtz resonator is composed of a cavity that