Helmholtz Resonance Frequency Research Articles

The evolution of air resonance power efficiency in the violin and its ancestors.

The fact that acoustic radiation from a violin at air-cavity resonance is monopolar and can be determined by pure volume change is used to help explain related aspects of violin design evolution. By determining the acoustic conductance of arbitrarily shaped sound holes, it is found that air flow at the perimeter rather than the broader sound-hole area dominates acoustic conductance, and coupling between compressible air within the violin and its elastic structure lowers the Helmholtz resonance frequency from that found for a corresponding rigid instrument by roughly a semitone. As a result of the former, it is found that as sound-hole geometry of the violin's ancestors slowly evolved over centuries from simple circles to complex f-holes, the ratio of inefficient, acoustically inactive to total sound-hole area was decimated, roughly doubling air-resonance power efficiency. F-hole length then slowly increased by roughly 30% across two centuries in the renowned workshops of Amati, Stradivari and Guarneri, favouring instruments with higher air-resonance power, through a corresponding power increase of roughly 60%. By evolution-rate analysis, these changes are found to be consistent with mutations arising within the range of accidental replication fluctuations from craftsmanship limitations with subsequent selection favouring instruments with higher air-resonance power.

Impedance assessment of a dual-resonance acoustic liner

Acoustic liners are commonly used to reduce noise from commercial aircraft engines. Engine liners are placed in the nacelle inlet and aft bypass duct to attenuate the noise radiated from the engine. Traditional engine liners are constructed of a perforated facesheet over a honeycomb structure to create a quarter-wave absorber. With this design, the low frequency performance of the liner is limited by the depth of the honeycomb. However, with advances in engine design, lower frequency sound absorption is becoming more critical while liner depth must be minimized. Acoustic metamaterials can exhibit unique acoustic behavior using periodically arranged sub-wavelength resonators. Researchers have shown that acoustic metamaterials can effectively block the propagation of low-frequency acoustic waves. Therefore, acoustic metamaterial-inspired concepts are being investigated to improve the low frequency performance of engine liners. A proposed dual-resonance liner is presented here that combines the idea of a Helmholtz resonator metamaterial with a traditional quarter-wave acoustic liner. The low frequency acoustic absorption of a traditional liner can be significantly increased by adding a second, low frequency resonance to the system. The normal incidence absorption coefficient of the proposed liner is more than 10 times larger than a conventional honeycomb liner at the designed Helmholtz resonance frequency while retaining similar performance at higher frequencies.

Numerical investigation for effects of actuator parameters and excitation frequencies on synthetic jet fluidic characteristics

Numerical investigation is performed to further address the effects of geometric parameters and excitation frequency of the actuator on the synthetic jet fluidic characteristics by utilizing a two-dimensional unsteady Reynolds-averaged Navier–Stokes model. The vibrating diaphragm is modeled as a movable wall varying in sinusoidal mode. Computations are carried out by using FLUENT software with the coupled user definition function (UDF) describing the diaphragm movement. The results show that the geometric parameters of the actuator, such as the cavity depth and diameter, as well as orifice thickness and diameter, have important influences on the synthetic jet fluidic characteristics. The velocity output could be maximized if the geometric parameters of the synthetic jet actuator are designed to ensure that the cavity acoustic Helmholtz resonance frequency is coincided with the diaphragm excitation frequency. For a fixed actuator cavity, when the diaphragm excitation frequency is consistent with the Helmholtz resonance frequency of actuator cavity, the relative pressure insides the cavity is obviously great during the ejection stroke while low during the suction stroke. In the presented actuator parameters, the synthetic jet is enhanced as the decrease of cavity depth for the fixed orifice. The change of cavity diameter in the vicinity of corresponding cavity acoustic resonance diameter has relatively weaker influence on the synthetic jet. When the diaphragm is excited at high frequency, small orifice diameter will restrict the ejection and suction capacity of the synthetic jet actuator.

Modeling and Experimental Validation of the Frequency Response of Synthetic Jet Actuators

A lumped-element mathematical model of the operation of a synthetic jet actuator driven by a thin piezoelectric disk is both analytically and numerically investigated to obtain information about the frequency response of the device. It is shown that the actuator behaves as a two-coupled oscillator system, and simple relationships are given to predict the two peak frequencies, corresponding to the modified Helmholtz and first-mode structural resonance frequencies. The model is validated through experimental tests carried out on three devices having different mechanical and geometrical characteristics, designed primarily to achieve an increasing coupling strength. A strict agreement between overall theoretical scaling laws and numerical computations is also found.

On the use of synthetic jet actuator arrays for active flow separation control

Present study highlights the flow control effectiveness of newly designed synthetic–jet–actuator (SJA) arrays placed at 23% and 43% of the chord from the leading edge of a low-speed wing model. First, the characteristics of a single SJA were investigated under the quiescent-flow condition. It was found that the jet velocity attains a peak between 400Hz and 500Hz, which corresponds to the SJA’s Helmholtz resonance frequency. The SJA arrays were then implemented on the wing model and investigated under the cross-flow condition. Both force balance and hot-wire measurements showed that the SJA arrays are able to effectively delay the flow separation and hence improve the aerodynamic performance of the wing model. The highest improvement in the lift coefficient is 27.4% and the average reduction in the drag coefficient is 19.6%. It was also found that the front (upstream) SJA array is more effective than its rear (downstream) counterpart. Tomographic-PIV measurements were also performed to unravel the three-dimensional flow details over the suction surface of the wing model with and without the SJA actuation. The time-averaged results showed that the introduction of synthetic jets substantially changes the flow structures of the separated shear layer, brings the outer high-momentum flow into the near-wall region, and delays the flow separation. In the end, the power consumption of a single SJA array was measured and found to be less than 5W.

20907 吸音材を内部に持つヘルムホルツ共鳴器による騒音低減

Helmholtz resonator is a device for noise reduction. It is effective for noise that has a dominant frequency component. However, in some other frequency components, Helmholtz resonator makes the sound pressure increase. In some cases, it is necessary to reduce the effective sound pressure. In this study, acoustic material is inserted to Helmholtz resonator for damping, and the resonator is applied to a sound tube for a basic study. As a result, the SPL is reduced using acoustic material. However, it is considered that the optimal reduction effect has not been obtained and it is necessary to change the resonant frequency of Helmholtz resonator. Next, the optimal value of the resonant frequency and the damping ratio of Helmholtz resonator is found, using identification of modal parameters and the theoretical formula of dynamic absorber's FRF.

Comparative numerical study of repulsive drift forces and gap resonances between two vessels floating side-by-side in proximity in head seas using a discontinuous HOBEM and a constant BEM with boundary matching formulation

The hydrodynamic interaction between two bodies floating side-by-side in close proximity was studied using a nine-node discontinuous higher order boundary element method based on the conventional two-body formulation (9dHOBEM) and a constant boundary element method based on the boundary matching formulation (BM-CBEM). It has been shown that unrealistic peaks on the first-order hydrodynamic coefficients at the first resonant frequency can be attenuated by both BM-CBEM combined with the free surface damping and 9dHOBEM combined with the wetted surface damping. It has also been shown that both the free surface damping and the wetted surface damping have apparent attenuation effects on the amplitude of radiation and scattering waves respectively at the first gap resonant frequency known as the Helmholtz resonant frequency. Almost perfect cancellations between the radiation and scattering waves in the gap between freely floating twin caissons in head seas have been found at the first two resonant frequencies. The significant peaks on the drift forces were found at the frequencies higher than the Helmholtz resonant frequency. Using 9dHOBEM and tuning the wetted surface damping parameter with experimental results, the unrealistically large numerical values of repulsive drift forces in head seas can be reduced reasonably.

Fluid-structure coupling effects in synthetic jet devices

The operation of a synthetic jet actuator driven by a thin piezoelectric disk is both analytically and numerically investigated by means of a lumped element mathematical model, in order to obtain information about the frequency response of the device. It is shown that the actuator behaves as a two-coupled oscillators system and simple relationships are given in order to predict the two peak frequencies, corresponding to the modified Helmholtz and first-mode structural resonance frequencies. The model is validated through experimental tests carried out on three devices having different mechanical and geometrical characteristics, designed primarily to achieve an increasing coupling strength. A strict agreement between overall theoretical scaling laws and numerical computations is also found.

Atmospherically Forced Exchange through the Bab el Mandeb Strait

Abstract The exchange between the Red Sea and the Indian Ocean on synoptic time scales (days to weeks) is investigated using moored current meter data collected in the strait of Bab el Mandeb from June 1995 to November 1996. Transport variations through the strait on these time scales can reach amplitudes of up to 0.6 Sv (1 Sv ≡ 106 m3 s−1), or nearly twice as large as the mean rate of exchange through the strait driven by annual evaporation over the Red Sea. The synoptic transport variability appears to be driven by two primary forcing mechanisms: 1) local wind stress variability over the strait and 2) variation in the large-scale barometric pressure over the Red Sea. Simple models of the forced response are developed and are shown to reproduce the essential features of the observations. The response to barometric pressure forcing over the Red Sea is fundamentally barotropic, whereas the response to along-strait winds is barotropic at high frequencies and tends toward a two-layer exchange at low frequencies. The responses to both types of forcing show enhanced amplitude at the Helmholtz resonance frequency for the Red Sea, which occurs at a period of about 5 days. A linear two-layer model, incorporating both types of forcing and a reasonable frictional parameterization, is shown to account for about 70% of the observed transport variance within the strait.

General Reduced-Order Model to Design and Operate Synthetic Jet Actuators

Synthetic jets are used in various applications from flow control to thermal management of electronics. Controlling the jet operating point using a simple voltage to velocity calibration becomes unreliable in case of external pressure field disturbances or varying actuator characteristics. This paper presents a general lumped parameter model for a synthetic jet actuator with an electromagnetic or piezoelectric driver. The fluidic model accurately predicts the synthetic jet operating point (i.e., Reynolds number and stroke length) based on the measured cavity pressure. The model requires only two empirical coefficients characterizing nozzle fluid damping and inertia. These can be obtained via calibration or estimated from pressure loss correlations and the governing acoustic radiation impedance. The model has been validated experimentally for circular and rectangular orifices. The effect of nozzle damping on the nonlinear system response is discussed. Analytical expressions are given for the two resonance frequencies characterizing the system response as a function of the diaphragm and Helmholtz resonance frequencies. The optimal design of an impinging synthetic jet actuator is discussed in terms of the thermal and acoustic efficiencies. Guidelines for selecting the optimum combination of diaphragm and Helmholtz resonance frequency are presented and compared with previous studies.

Radiation characteristics of multiple and single sound hole vihuelas and a classical guitar

Two recently built vihuelas, quasi-replicas of the Spanish Renaissance guitar, one with a small body and one sound hole and one with a large body with five sound holes, together with a classical guitar are investigated. Frequency dependent radiation strengths are measured using a 128 microphone array, back-propagating the frequency dependent sound field upon the body surface. All three instruments have a strong sound hole radiation within the low frequency range. Here the five tone holes vihuela has a much wider frequency region of strong sound hole radiation up to about 500 Hz, whereas the single hole instruments only have strong sound hole radiations up to about 300 Hz due to the enlarged radiation area of the sound holes. The strong broadband radiation of the five sound hole vihuela up to about 500 Hz is also caused by the sound hole phases, showing very consistent in-phase relations up to this frequency range. Also the radiation strength of the sound holes placed nearer to the center of the sound box are much stronger than those near the ribs, pointing to a strong position dependency of sound hole to radiation strength. The Helmholtz resonance frequency of the five sound hole vihuela is influenced by this difference in radiation strength but not by the rosettas, which only have a slight effect on the Helmholtz frequency.

Helmholtz resonance in a piezoelectric–hydraulic pump-based hybrid actuator

This paper demonstrates that a hydraulically acting Helmholtz resonator can exist in apiezoelectric–hydraulic pump (PHP) based hybrid actuator, which in turn affects thevolumetric efficiency of the PHP. The simulation and experimental results illustrate theeffect of Helmholtz resonance on the flow rate performance of the PHP. The study alsoshows how to shift the Helmholtz resonant frequency to a higher value through changingparameters such as the cylinder diameter and the effective bulk modulus of the workingfluid, which will improve the volumetric efficiency and broaden the operating frequencyrange of the PHP actuator.

Lumped element modelling of synthetic jet actuators

In this paper, a lumped element model of synthetic jet actuator is presented and used to predict the temporal variation of the jet velocity. Unlike the previous model reported in the literature, in this model the mechanical movement of the diaphragm is decoupled from the fluid phenomenon in the actuator cavity to allow the modelling of fluid mechanics aspect of the actuator to be investigated and validated separately. Furthermore, the “minor losses” occurring at the orifice exit is included and linked to the jet exit velocity profile. The results from this model are validated using the existing experimental data and CFD simulations. It is found that this model is capable of predicting the temporal variation of synthetic jets both in phase and magnitude when the actuator is operating away from the Helmholtz resonance frequency. Although the model fails to predict the correct phase information at the Helmholtz resonance frequency, it can still produce the jet peak velocity that is in good agreement with the experimental data. The lumped element model presented in this paper can be used to provide a reliable prediction of the jet peak velocity needed in the initial design of synthetic jet actuators for practical applications.

Helmholtz resonator experiment for Project Listen Up.

The behavior of sound waves and resonant effects can be observed using Helmholtz resonators. Resonators are built from identical round wooden boxes purchased from a craft store. The tops are glued and drilled with hole diameters from 2–3 cm. We can study the resonant behavior as a function of hole diameter only. The end effect is large compared with the thickness of the orifice (0.6 cm). In the experiment, a swept tone (100–900 Hz) from a small speaker drove the resonator. One studied the output of the microphone located near the orifice. One could use a swept spectrum analyzer, a function generator, or tuning fork with varying weights to measure the resonant frequency of the box. A plot of hole diameter versus frequency can be compared with the theoretical Helmholtz resonant frequency prediction, which depends on the volume of the box, the cross sectional area, the sound speed of air, and the effective length of the hole. One can model the effective length of the resonator as the thickness of the top plu...

Influence of cavity wall elasticity on resonant frequency of small underwater cylindrical Helmholtz resonator

Influence of cavity wall elasticity on resonant frequency of small underwater cylindrical Helmholtz resonator is studied theoretically and experimental. Based on the theory of electroacoustic analogy, the simplified low frequency lumpedparameter model of the Helmholtz resonator is constructed. A general, convenient for calculation expression of the resonant frequency is given by circuit analysis. The influence of the thickness and the material of the resonator on the resonant frequency is investigated by numerical method. And the approximate rigid conditions for small underwater cylindrical Helmholtz resonators of different sizes are given. Small cylindrical Helmholtz resonators of different wall thickness and material were tested in a standingwave tube filled with water. Experimental results well testified the theoreticl results and the approximate rigid condition. This paper is useful for the design and application of the underwater cylindrical Helmholtz resonators.

Resonant frequency of an adjustable Helmholtz resonator in a hydraulic system

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.

Harmonicity of trumpet modes

The mouthpiece on a brass instrument is generally removable but constitutes an important part of the whole instrument. In the frequency domain, it can be considered to provide a frequency dependent equivalent length that increases with frequency up to the Helmholtz resonance frequency fpop of the mouthpiece itself. Geometrical changes that affect the total volume or the fpop of the mouthpiece will affect the harmonicity of the nearly harmonic normal modes of the instrument. Using heterodyne filter analysis, the development of the frequency components and their amplitudes were measured for low trumpet notes, both for repeated attacks of short notes and for sustained note crescendos from pianissimo to fortissimo. The measurements were repeated after the mouthpiece was modified to improve the harmonicity of the normal modes. During both attack and crescendo tests, the modified mouthpiece was associated generally with more stable frequencies of the partials and more even development of the amplitudes of the partials.

A pressure-based estimate of synthetic jet velocity

Synthetic jets are used for active flow control and enhanced heat transfer, and are typically generated by an orifice connected to a cavity with movable diaphragm actuator. Low-power operation is achieved by matching actuator and Helmholtz resonance frequencies. This brief communication presents an analytical model derived from simplified gas dynamics, for estimating the synthetic jet velocity and actuator deflection, based on a cavity pressure measurement. Model closure is provided by a damping force in the orifice, which agrees with established pressure loss correlations for steady flow through short ducts. The model is validated against experimental data obtained for an axisymmetric synthetic jet. The valid frequency range extends from zero, over the Helmholtz resonance frequency, up to a geometry-dependent limit frequency. This model presents a reference against which synthetic jet velocity can be calibrated.

Fluid Dynamics-Based Analytical Model for Synthetic Jet Actuation

An analytical model for synthetic jet actuation based on the laws of fluid dynamics is presented. A synthetic jet actuator consists of a cavity with a driven wall and an orifice. Under actuation, the wall is oscillated, resulting in an oscillatory flow through the orifice. In the model, the driven wall is modeled as a single-degree-of-freedom mechanical system, which is pneumatically coupled to the cavity-orifice arrangement acting as a Helmholtz resonator. The latter was modeled using the unsteady form of the continuity and Bernoulli equations with a loss term. The model was validated against experimental data available in the published literature, and very good agreement is obtained between the predicted and measured frequency responses as well as for the phase relationships between velocities and pressures. The model and analysis based on it provide valuable insights into the behavior of synthetic jet actuators and reveal that air in the actuator cavity exhibits compressibility at all frequencies beyond the Helmholtz resonance frequency.

Internal and net envelope pressures in a building having quasi-static flexibility and a dominant opening

This paper describes a study on the influence of the flexibility of building envelope on pressures inside and net pressures on the roof of low-rise buildings with a dominant opening. It is shown that building flexibility lowers the Helmholtz resonance frequency and increases damping in the internal pressure system as indicated by the lowering of the resonant peak in the internal pressure admittance function. Consequently, it was found that the flexibility of the building reduces fluctuations in internal and net envelope pressures, as indicated by somewhat smaller RMS pressure coefficients relative to the case of a rigid building.