Helmholtz Resonators: One-Dimensional Limit for Small Cavity Length-to-Diameter Ratios

Dickey, N. S.; Selamet, Ahmet

doi:10.1006/jsvi.1996.0440

Cited by 55 publications

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“…In a later paper, Dickney and Selamet [10] studied resonators having small cavity length-to-diameter ratios and pointed out the e!ect of radial propagation on the natural frequency and transmission loss.…”

Section: Introductionmentioning

confidence: 99%

A Simple Method for the Analysis of Deep Cavity and Long Neck Acoustic Resonators

Doria

2000

Journal of Sound and Vibration

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Section: Introductionmentioning

confidence: 99%

A Simple Method for the Analysis of Deep Cavity and Long Neck Acoustic Resonators

Doria

2000

Journal of Sound and Vibration

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“…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 is connected to the surroundings through a narrow neck or through an opening [1,6,10] (Fig. 1).…”

Section: Introductionmentioning

confidence: 99%

Resonant frequency of an adjustable Helmholtz resonator in a hydraulic system

Kela

2008

Arch Appl Mech

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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.

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“…Cummings (1992), Doria (1995), Fahy & Schofield (1980), and Li & Cheng (2007) successfully assessed the resonant frequency for an enclosure that was composed of the HR device. Dickey and Selamet (1996) analyzed the resonant frequency of a non-symmetric chamber using a three-dimensional boundary element method. Chanaud (1997) assessed the influence of the resonant frequency with respect to various locations of a resonating tube; additionally, he studied the influence of the resonant frequency for a rectangular chamber with a square opening.…”

Section: Introductionmentioning

confidence: 99%

Noise Elimination of a Multi-tone Broadband Noise with Hybrid Helmholtz Mufflers Using a Simulated Annealing Method

Chiu¹

2012

Archives of Acoustics

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Noise control is essential in an enclosed machine room where the noise level has to comply with the occupational safety and health act. In order to overcome a pure tone noise with a high peak value that is harmful to human hearing, a traditional reactive muffler has been used. However, the traditional method for designing a reactive muffler has proven to be time-consuming and insufficient. In order to efficiently reduce the peak noise level, interest in shape optimization of a Helmholtz muffler is coming to the forefront.Helmholtz mufflers that deal with a pure tone have been adequately researched. However, the shape optimization of multi-chamber Helmholtz mufflers that deal with a broadband noise hybridized with multiple tones within a constrained space has been mostly ignored. Therefore, this study analyzes the sound transmission loss (STL) and the best optimized design for a hybrid Helmholtz muffler under a spaceconstrained situation. On the basis of the plane wave theory, the four-pole system matrix used to evaluate the acoustic performance of a multi-tone hybrid Helmholtz muffler is presented. Two numerical cases for eliminating one/two tone noises emitted from a machine room using six kinds of mufflers (muffler A∼F) is also introduced. To find the best acoustical performance of a space-constrained muffler, a numerical assessment using a simulated annealing (SA) method is adopted. Before the SA operation can be carried out, the accuracy of the mathematical model has been checked using the experimental data. Eliminating a broadband noise hybridized with a pure tone (130 Hz) in Case I reveals that muffler C composed of a onechamber Helmholtz Resonator and a one-chamber dissipative element has a noise reduction of 54.9 (dB). Moreover, as indicated in Case II, muffler F, a two-chamber Helmholtz Resonator and a one-chamber dissipative element, has a noise reduction of 69.7 (dB). Obviously, the peak values of the pure tones in Case I and Case II are efficiently reduced after the muffler is added.Consequently, a successful approach in eliminating a broadband noise hybridized with multiple tones using optimally shaped hybrid Helmholtz mufflers and a simulated annealing method within a constrained space is demonstrated.Keywords: multiple tones, hybrid, Helmholtz, four-pole transfer matrix method, SA method. p -acoustic pressure (Pa), p% -the porosity of the perforated tube in the dissipative element, Q -volume flow rate of venting gas (m 3 s −1 ), r k -the radius of the resonating tube in the Helmholtz resonator (m), Rres -the acoustic resistance, SA -simulated annealing, S i -the section area at the i-th node (m 2 ), Archives of Acoustics -Volume 37, Number 4, 2012 S k -the section area of the resonating tube in the Helmholtz resonator (m 2 ), STL -sound transmission loss (dB), SWL T -overall sound power level inside the muffler's output (dB), T * ij -components of a four-pole transfer system matrix, TS ij , TSC ij , TSE ij , THR ij -components of four-pole transfer matrices for an acoustical mechanism with a s...

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Helmholtz Resonators: One-Dimensional Limit for Small Cavity Length-to-Diameter Ratios

Cited by 55 publications

References 0 publications

A Simple Method for the Analysis of Deep Cavity and Long Neck Acoustic Resonators

A Simple Method for the Analysis of Deep Cavity and Long Neck Acoustic Resonators

Resonant frequency of an adjustable Helmholtz resonator in a hydraulic system

Noise Elimination of a Multi-tone Broadband Noise with Hybrid Helmholtz Mufflers Using a Simulated Annealing Method

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