Theoretical and experimental study of coupled Helmholtz resonators

Frequency-specific highly sensitive acoustic sensor using a piezoresistive cantilever element and parallel Helmholtz resonators

Resonance frequencies and sound absorption of Helmholtz resonators with multiple necks

Improved calculation of resonant frequencies of Helmholtz resonators

Some kinds of thermofluid instruments are using Helmholtz resonators for absorbing noises radiated from them. Since the resonance frequency of a Helmholtz resonator depends on the ratio of the resonant volume to the neck size, operating frequency range can be easily tuned and thus the Helmholtz resonator is well-suited for noise control in a wide range of frequency. Besides the noise control application, Helmholtz resonators have been recently applied to acoustic energy harvesting. To date, most of studies on energy harvesting using Helmholtz resonators are employing piezoelectric materials located in the resonant volume and enhancing harvesting efficiency by tuning the resonance frequency and the structure of the added piezoelectric materials. In this study, a piezoelectric (PVDF composite) cantilever was integrated within a Helmholtz resonator. Then, energy harvesting efficiency was maximized by matching and tuning mechanical resonance of the piezoelectric cantilever and acoustic resonance of the Helmholtz resonator. Theoretical analysis including finite element simulation was also performed to confirm our experimental results. To maximize the harvest power, the electrical impedance matching was considered. This study can be applied to acoustic energy harvesting as well as acoustic noise control.

Helmholtz resonators are commonly used to damp thermoacoustic oscillations in aeroengine and gas turbine combustors. In practice, the Helmholtz resonator is often maintained at a cooler temperature than the combustor, but this tends to be neglected when modeling. In this work, we derive an analytical model for both the acoustic damping and the effect on the combustor thermoacoustics of Helmholtz resonators for which the volume is at a different temperature to the combustor. The energy conservation equation based on stagnation enthalpy, together with the mass and momentum conservation equations, is incorporated into a linear Helmholtz resonator sound-absorption model. These are coupled with linear wave-based models for the plane acoustic waves in the system to which the Helmholtz resonator is attached: here, a combustor. The temperature difference is found to generate an entropy wave that advects downstream of the resonator (and may generate further acoustic waves if accelerated) and to change the acoustic damping near the resonant frequency. This model for the Helmholtz resonator acoustics is then incorporated into a low-order network model for combustor thermoacoustics. The importance of capturing the effect of the Helmholtz resonator temperature difference on the overall thermoacoustic modes is clearly demonstrated.

This paper reports an acoustic sensor using a Helmholtz resonator (HR) array and a MEMS differential pressure (DP) sensor element. A piezoresistive cantilever type DP sensor is highly sensitive to acoustic waves around its mechanical resonant frequency (RF). By attaching a HR array of which RF is equal to the cantilever in front of the DP sensor like a cap, the sensitivity is enhanced at the RF. The developed sensor with the HR responded with 3 times higher sensitivity than without the HR, and realized a resolution of approximately 2 mPa without an electrical lock-in filter.

Computational study of an incident shock wave into a Helmholtz resonator

Liquid volume measurement with a closed Helmholtz resonator under micro-gravity conditions

In this paper we carried out the simulation for controlling the resonance frequency of a Helmholtz resonator, which is used for the reduction of noise. The resonance frequency is designed to the desired value by PID control of the acoustical boundary condition of the Helmholtz resonator. The resonator like this is called Smart Helmholtz Resonator. At first the gains of PID controller is changed to several values and it is confirmed that the resonance frequency is varied. In order to realize the desired resonance frequency, the gains of PID controller are determined by the response surface method. By using the response surface method the determination of the optimal gains are possible for a lower frequency region accurately. It is shown that this method is effective for designing the resonance frequency of Smart Helmholtz Resonator.

Aiming at the unsatisfactory low-frequency sound absorption effect of Helmholtz resonator, a novel broadband low-frequency ventilation absorber with rough neck is proposed. The roughness is introduced into the neck of Helmholtz resonator to change the shape of the neck and achieve the structure of rough neck Helmholtz resonator. The proposed absorber can effectively provide the acoustic impedance required for low-frequency sound absorption without changing the overall size, thereby reducing the resonant frequency. The finite element method is used to simulate the structure, and the impedance tube sound absorption test is carried out to verify it. The experimental and simulation results show high consistency with each other. The results also indicate that the rough neck Helmholtz resonator absorber with roughness introduced in the neck achieves an absorption peak at 58 Hz, with an absorption coefficient of about 0.63. Comparing with the absorber without roughness introduced, the resonant peak frequency becomes low, from 70 Hz to 58 Hz, reducing 17.1%. Therefore, adjusting the neck roughness can serve as a method of tuning the acoustic performance, and the absorption peak frequency can be adjusted by appropriately increasing the neck roughness so as to move it in the low frequency direction. Based on the verification that the roughness of the neck can effectively reduce the absorption peak frequency of Helmholtz resonator, a broadband low-frequency ventilation absorber with a rough neck, which is composed of eight absorption units, is designed. Through simulation calculation and experimental exploration, the absorption coefficient can achieve more than 0.8 in a target working frequency band of 500－1100 Hz. On this basis, the acoustic impedance of the structure can be adjusted by introducing roughness into the neck of Helmholtz resonator, so as to obtain the optimized broadband low-frequency ventilation absorber with a rough neck, which achieves a broadband sound absorption coefficient higher than 0.8 in a frequency range of 400–1200 Hz. The optimized structure also has 8 consecutive absorption peaks with amplitudes above 0.95. The proposed low-frequency broadband ventilation absorber provides a reference for designing and optimizing efficient low-frequency subwavelength acoustic absorbers. It has a wide range of applications in pipeline noise control.

A programmable resonator based on a shunt-electro-mechanical diaphragm

This work presents a study of estimating material volumes in an oblique cylindrical silo using acoustic impulses and broadband waves. Silo as an acoustical, linear and time-invariant system was assumed and frequency response of the system can be determined. Three types of system excitations, acoustic impulses, white and pink noises were used. The acoustic impulses were generated from a silo-knocking mechanism, controlled by a microcontroller and computer. White and pink noises were generated using computer programming and fed to a loudspeaker in the silo via a sound interface and power amplifier. Acoustic waves in the silo were gathered by a microphone and digitally processed for extracting the silo's frequency responses in frequency domain. The resonance frequencies and corresponding mode numbers were used to calculate a length of air cavities in the cylindrical silo. With known dimension of the silo, volumes of remaining materials can be obtained. Experimentations were done to estimate volumes of cement, sand, and water in a laboratory-sized cylindrical silo. Results showed that the acoustic impulse excitation only yielded volume estimates for certain volume levels and their estimation errors were quite high. Material volume estimations obtained by using white and pink noise excitation yielded very satisfactory accuracy. Averaged error percentages for estimations of cement, sand, and water volume were 0.67%, 1.27% and 1.05% when the white noise was used, and 1.31%, 1.13% and 1.64% when the pink noise was utilized, respectively.

As one of the most fundamental processes, excited-state proton transfer (ESPT) plays a major role in both chemical and biological systems. In the past several decades, experimental and theoretical studies on ESPT systems have attracted considerable attention because of their tremendous potential in fluorescent probes, biological imaging, white-light-emitting materials, and organic optoelectronic materials. ESPT is related to fluorescence properties and usually occurs on an ultrafast time scale at or below 100 fs. Consequently, steady-state and femtosecond time-resolved absorption, fluorescence, and vibrational spectra have been used to explore the mechanism of ESPT. However, based on previous experimental studies, direct information, such as transition state geometries, energy barrier, and potential energy surface (PES) of the ESPT reaction, is difficult to obtain. These data are important for unravelling the detailed mechanism of ESPT reaction and can be obtained from state-of-the-art ab initio excited-state calculations. In recent years, an increasing number of experimental and theoretical studies on the detailed mechanism of ESPT systems have led to tremendous progress. This Account presents the recent advances in theoretical studies, mainly those from our group. We focus on the cases where the theoretical studies are of great importance and indispensable, such as resolving the debate on the stepwise and concerted mechanism of excited-state double proton transfer (ESDPT), revealing the sensing mechanism of ESPT chemosensors, illustrating the effect of intermolecular hydrogen bonding on the excited-state intramolecular proton transfer (ESIPT) reaction, investigating the fluorescence quenching mechanism of ESPT systems by twisting process, and determining the size of the solute·(solvent) n cluster for the solvent-assisted ESPT reaction. Through calculation of vertical excitation energies, optimization of excited-state geometries, and construction of PES of the ESPT reactions, we provide modifications to experimentally proposed mechanisms or completely new mechanism. Our proposed new and inspirational mechanisms based on theoretical studies can successfully explain the previous experimental results; some of the mechanisms have been further confirmed by experimental studies and provided guidance for researchers to design new ESPT chemosensors. Determination of the energy barrier from an accurate PES is the key to explore the ESPT mechanism with theoretical methods. This approach becomes complicated when the charge transfer state is involved for time-dependent density functional theory (TDDFT) method and optimally tuned range-separated TDDFT provides an alternative way. To unveil the driving force of ESPT reaction, the excited-state molecular dynamics combined with the intrinsic reaction coordinate calculations can be employed. These advanced approaches should be used for further studies on ESPT systems.

The reflection of linearly polarized electromagnetic plane waves from an N-layer system of inhomogeneous, dielectric films on a transparent, homogeneous substrate is investigated in the long-wavelength limit. Approximate formulas are obtained for changes in the reflectance of s- or p-polarized light and in the ellipsometric angles that are caused by a multilayer, thin-film system. An analysis of the influence of a multilayer, ultrathin surface film on the reflectance of p-polarized light at the Brewster angle is carried out. All approximate analytical results are correlated with the exact computer solution of the reflection problem for a multilayer system of inhomogeneous films. The possibilities are discussed of using the obtained approximate expressions for resolving the inverse problem of ultrathin dielectric films on transparent substrates. Novel options are developed for determining the parameters of ultrathin films by integrating differential reflectance and ellipsometry.

The influence of the grazing flow and sound incidence direction on the acoustic characteristics of double Helmholtz resonators