Coupled Helmholtz Resonators Research Articles

Noise-insulating structures based on supercells and chirped lattices enhanced via tuning of local coupling

Acoustic metamaterials and phononic crystals have proven themselves to be highly promising for the development of next-level noise-mitigation systems. One of the main challenges limiting the implementation of such structures is a typically narrow operational frequency range. In this work, we consider a periodic system consisting of locally coupled Helmholtz resonators and demonstrate that positions and widths of stop-bands can be adjusted via tuning of the coupling strength. Several approaches are developed, including the introduction of the chirped structures, supercells, or resonators with enhanced intrinsic losses. We numerically and experimentally demonstrate that tuning of local coupling leads to a merging of stop-bands, resulting in broadband noise-insulation within the operational range covering about 3.5 octaves. This property is linked to band structures of the associated infinitely periodic structures and discussed in terms of band-gap engineering. The low filling factor of the unit cells also suggests that the considered structures can be ventilated, which is demonstrated numerically.

Acoustic bound states in the continuum in coupled Helmholtz resonators

Acoustic bound states in the continuum in coupled Helmholtz resonators

Meta-structure based on coupled resonators for low-frequency broadband sound absorption

This work investigates and explains the behavior of an acoustic meta-structure based on different coupled Helmholtz resonators (HR). The analytical formulation of the Maa model is used to represent both the acoustic impedance and the sound absorption mechanism of the absorber. The structures are numerically modeled using finite element method and validated experimentally in an impedance tube considering sound waves of normal incidence. The absorber samples were manufactured in ABS (acrylonitrile butadiene styrene) polymer material with the additive manufacturing technique by extrusion of material. The results of the impedance tube, numerical and theoretical tests showed agreement and the sound absorber showed a sub-wavelength scale with perfect sound absorption ( 0.97) and broadband of 292 Hz in the low frequency region (200 - 600 Hz). We deduced that the excellent experimental result obtained is due to the high resolution used in the sample manufacturing (± 0.1 mm) which minimized manufacture errors. Finally, the influences of the main parameters of the HR panel (width and depth of the micro-slit) on the sound absorption coefficient of the absorber were also analyzed.

Broadband noise-insulating periodic structures made of coupled Helmholtz resonators

Acoustic metamaterials and phononic crystals represent a promising platform for the development of noise-insulating systems characterized by a low weight and small thickness. Nevertheless, the operational spectral range of these structures is usually quite narrow, limiting their application as substitutions of conventional noise-insulating systems. In this work, the problem is tackled by demonstration of several ways for the improvement of noise-insulating properties of the periodic structures based on coupled Helmholtz resonators. It is shown that tuning of local coupling between the resonators leads to the formation of a broad stopband covering ∼3.5 octaves (200–2100 Hz) in the transmission spectra. This property is linked to band structures of the equivalent infinitely periodic systems and is discussed in terms of bandgap engineering. The local coupling strength is varied via several means, including introduction of chirped structures and lossy resonators with porous inserts. The stopband engineering procedure is supported by genetic algorithm optimization, and the numerical calculations are verified by experimental measurements.

The influence of structural changes and defects on noise mitigation properties of the periodic structures based on coupled Helmholtz resonators

The work is dedicated to investigation of several ways for optimization of periodic structures based on coupled Helmholtz resonators. Such modifications as chirped lattices, arbitrary defects, and supercells, are explored. We analyze widening of stop-bands associated with the introduction of these structural changes and how they affect the corresponding noise mitigation properties. Utilizing numerical calculations we find optimal parameters of the considered structures and study the dependence of transmission coefficient on various geometric parameters of the system. As a main result, we demonstrate the merging of several stop-bands leading to ultra-broadband noise mitigation. The achieved enhancement is linked to the properties of the equivalent infinite structures and their eigenmodes.

Design of coupled Helmholtz resonator with rectangular enclosure to mitigate low frequency noise in recording booths

This study summarizes theoretical and experimental findings for low frequency noise mitigation in small recording booths using coupled Helmholtz resonators. The room acoustical resonance modes were identified using ANSYS simulation software for the recording booth. An experimental setup validated the existence of the different low frequency modes and variation from theoretical results due to the enclosure wall's surface material. Microphone and speaker system were used to measure the room frequency response at the resonant frequencies. Piezoelectric sensors were placed at different positions within the room to determine the location of resonance peaks and the optimized position for the coupled Helmholtz resonator. The effects of damping on the Helmholtz resonator frequency response and deviation from theoretical design formulae were explored. The resonator apparatus proved to attenuate noise to half as loud in the selected low frequency range within the recording booth.

Sound absorption using sonic crystals with coupled Helmholtz resonators

Sonic crystals are made up of a periodic arrangement of sound scatterers and absorbers that exhibit band-gap behaviour, allowing them to block out certain band of frequencies of sound (Bragg's law). This allows artificially engineered structures, through proper design of geometry and placements of scatterers, to achieve specific acoustic properties for sound absorption and noise mitigation. Embedding Helmholtz resonators into sonic crystals have been shown to improve the low-frequency attenuation performance as a combined system. In this study, we investigated the interaction of coupled Helmholtz resonators within a sonic crystal. Parametric studies were conducted using the finite element method on the spectral insertion loss of these sonic crystals with various arrangements of the Helmholtz resonators. The results show that sharp attenuation at specific frequencies may be achieved by proper tuning of these resonators, improving the low-frequency performance of the sonic crystals as a broadband sound absorber.

Low frequency sound isolation by a metasurface of Helmholtz ping-pong ball resonators

We study both numerically and experimentally an acoustic metasurface based on coupled Helmholtz resonators to obtain broadband low-frequency spectral responses for acoustic insulation. A hierarchical approach is proposed, starting from single and coupled Helmholtz resonators, up to a periodic array of resonators. To this end, we performed numerical simulations using the finite element method, in which the resonators are modeled as drilled rigid spheres in airborne environment and experimental demonstrations based on ping-pong balls as Helmholtz resonators in an acoustic reverberation box. We showed the alteration of the low-frequency response of acoustic insulation resulting from inter-unit coupling in acoustic metasurfaces, and the apparition of additional attenuation by inserting a plexiglass board as support for the structure.

Broadband quasi-perfect sound absorption by a metasurface with coupled resonators at both low- and high-amplitude excitations

This study presents an acoustic metasurface (AM) consisting of coupled Helmholtz resonators with extended necks (HRENs) to effectively absorb broadband sound waves at both low and high amplitudes. A nonlinear acoustic model is proposed to characterize the AM performance based on the equivalent medium theory and the transfer matrix method. The nonlinear effects due to the high-amplitude excitation are considered by a velocity-dependence equivalent density of the air in the neck. The acoustic characteristics of an AM with two coupled HREN units at the sound pressure level (SPL) ranging from 100dB to 140dB are analytically, numerically, and experimentally investigated. Results from the three approaches show good agreement. The AM achieves quasi-perfect absorption (absorption coefficient α>0.9) in a wide range of SPL, while each HREN unit alone only performs well at around 130dB. The superior absorption performance of the AM at relatively low-amplitude excitation originates from the coherent coupling effects between adjacent units. With the increase of the sound level, the coupling effects tend to deteriorate; fortunately, the sound-vortex conversions occur, contributing to additional acoustic dissipation and thereby sustaining the quasi-perfect absorption capability. Based on the absorption mechanisms, a broadband AM with multiple coupled resonators is designed and manufactured. The measured averaged absorption coefficient of the AM is larger than 0.91 at the SPL below 140 dB (α>0.97 at 100dB) within [700,1100]Hz, and the compact thickness is of 1/18 wavelength at the lowest operating frequency. The findings in this study offer a promising approach to achieve highly efficient broadband sound absorption in a wide-ranging noise level, which holds great potentials in practical applications for noise control.

Coupled Helmholtz Resonators with Multiple Resonant Modes for Fano‐Like Interferences

Herein, the Helmholtz resonance modes design is developed obtaining Fano‐like interferences. The proposed design employs two vertically aligned Helmholtz resonators exciting two different orders of mode, which induce desired constructive or destructive interferences. The critical part of this design is the realization of a mode‐selective feature. The mode‐selective feature is achieved by adjusting the geometrical parameters of the two Helmholtz resonators. Meanwhile, it can be constructed by applying different mediums under the symmetrical geometric topology. From the numerical simulation results, desired modes can be excited at desired resonant frequencies achieving constructive or destructive interferences. These Fano‐like phenomena are also confirmed by experimental results.

Lightweight panels based on Helmholtz resonators for low-frequency acoustic insulation

In this study, we propose a novel lightweight acoustic metamaterial panel composed of coupled Helmholtz resonators, designed to insulate low-frequency broadband noises effectively. Through finite element analysis, we observe the emergence of band gaps with varying widths, depending on the unit cell dimensions, the band gaps start at 100 Hz, and as the scale decreases, the band gaps shift to higher frequencies within specific ranges. These band gaps arise from the coupling of two Helmholtz resonators with different volumes but a common neck. For our work, we use ABS materials, which facilitate easy panel manufacturing. Moreover, we also explored the potential of other materials to enhance the low-frequency broadband sound insulation performance of the system. The results obtained from this research provide promising insights into developing lightweight panels for efficient low-frequency broadband sound insulation.

Case studies on aeroacoustics damping performances of Coupled Helmholtz Resonators over low frequency ranges

Helmholtz resonators are widely applied in industries to reduce the transmission of unwanted noise and passively attenuate tonal noise in pipes/ducts. For example, internal combustion engines take advantage of Helmholtz resonators by combining air box, subwoofers and perforated pipes/plates to reduce engine noise emission nowadays. However, the main drawback of the conventional Helmholtz resonators includes a very narrow bandwidth. To broaden the effective noise damping frequency range of Helmholtz resonators, a number of different improved designs are reported and tested recently in the literature such as applying an array of separated resonators or implementing mechanical-coupled Helmholtz resonators. In this work, we conduct a brief review on the aeroacoustics damping performance of coupled Helmholtz resonators over low frequency range. The noise damping performances could be characterized and quantified in terms of transmission loss and sound absorption coefficient. Both definitions are discussed. Comparison is then made between the separately working resonators and the mechanical-coupled ones. This is achieved by replacing the sharable flexible sidewall with a rigid sidewall. The effect of the mean grazing flow is also discussed and examined on the noise damping performances. An experimental case study of the present authors is included. Additionally, to improve the noise damping performance further, an overview of the resonators neck with different noise damping materials inserted is conducted. Finally, 3D numerical approaches in simulating the aeroacoustics damping performances of coupled Helmholtz resonators are reviewed. This case study and brief overview provides a guidance on improving the design of coupled Helmholtz resonators and an array of Helmholtz resonators.

Reduction of the occlusion effect induced by earplugs using quasi perfect broadband absorption

Passive earplugs are used to prevent workers from noise-induced hearing loss. However, earplugs often induce an acoustic discomfort known as the occlusion effect. This phenomenon corresponds to an increased auditory perception of the bone-conducted part of physiological noises at low-frequency and is associated with the augmentation of the acoustic pressure in the occluded earcanal. In this work, we report a new concept of passive earplugs for mitigating the occlusion effect between 100 Hz and 1 kHz. The strategy consists in reducing the input impedance of the earplug seen from the earcanal by using quasi-perfect broadband absorbers derived from the field of meta-materials. The proposed “meta-earplug” is made of 4 critically coupled Helmholtz resonators arranged in parallel. Their geometry is optimized using an evolutionary algorithm associated with a theoretical model of the meta-earplug input impedance. The latter is validated against a finite-element approach and impedance sensor measurements. The meta-earplug is manufactured by 3D printing. Artificial test fixtures are used to assess the occlusion effect and the insertion loss. Results show that the meta-earplug induces an occlusion effect approximately 10 dB lower than foam and silicone earplugs while it provides an insertion loss similar to the silicone earplug up to 5 kHz.

Single and coupled Helmholtz resonators for low frequency sound manipulation

In this work, we use the finite element method to study the acoustic properties of single and coupled Helmholtz resonators (HRs). Each HR consists of a sphere drilled with one or several small openings. For a single HR, we show that the total pressure computed at the opening's edge as a function of frequency reveals the presence of a local dip in addition to the well-known resonance peak. In the case of coupled resonators, we highlight two resonance peaks at low frequencies, arising from excitation of a monopolar breathing mode, for which the twin resonators are in phase (S-peak), and a dipolar mode, where the two spheres resonate out of phase (AS-peak). In the near field, we study the influence of the number of apertures, the distance between spheres and their orientation on the frequencies, and quality factors of the two resonances. In the far field, we show that the propagation of the scattered wave is quasi-isotropic for the S-peak, while it leads to a dipolar-type pressure distribution for the AS-peak, with a directionality depending on the relative orientation of the openings in adjacent HRs. By increasing the number of coupled HRs from two to four units, we investigate the effect of additional mode coupling. Accordingly, the present study aims to manipulate the sound at targeted frequencies, by varying the distance or orientation between twin resonators, and to discuss the effect of dissipation. The demonstration of the coupling between sub-wavelength units opens the way to multi-frequency functionalities of acoustic metasurfaces.

Experimental investigation of geometric shape effect of coupled Helmholtz resonators on aeroacoustics damping performances in presence of low grazing flow

Helmholtz resonators are widely used as acoustic dampers to mitigate noise in gas turbines and automotive exhaust systems. In order to increase the damping performance and broaden the damping frequency range, multiple Helmholtz resonators are typically implemented. In this work, two connected Helmholtz resonators by sharing the same flexible or rigid sidewall, i.e. parallel-coupled are designed and tested on a cold-flow pipe system with a mean flow present. Two different geometric shapes of the coupled Helmholtz resonators are considered. One is cylindrically shaped and the other is rectangular. Both experimental and 3D numerical investigations are conducted to study the effects of the geometric shape and the mean grazing flow on the noise damping performance of the resonators. The numerical model is built in frequency-domain and solving linearized Navier-Stokes equations. To characterize and quantify the resonators' noise damping performance, transmission loss in dB is determined. It is experimentally found that the cylindrical shaped resonators are associated with much larger transmission loss. Compared with the rectangular-shaped resonators, approximately 12 dB more sound pressure level reduction is achieved by the cylindrical resonators, which is independent on the rigidness of the shared sidewall. The rigidity of the shared sidewall is shown to shift the frequencies corresponding to the maximum damping peaks, depending on the sidewall's flexural rigidity. Numerical results confirm that the geometric shape does play an important role in determining the resonator's damping. Further investigation of the mean grazing flow effect is conducted. It is shown experimentally and numerically that when the Mach number of the mean grazing flow is lower than 0.01, the noise damping performance of the coupled Helmholtz resonators is little changed over the frequency range from 150 to 600 Hz. However, as the mean flow Mach number is increased, the damping performance becomes deteriorated as observed numerically. The present work reveals the critical roles played by the geometric shape and the mean grazing flow on the aeroacoustics damping performance of the coupled-resonators.

Broadband acoustic double-zero-index cloaking with coupled Helmholtz resonators

Acoustic double-zero-index metamaterials (DZIM) characterized by extremely large phase velocity along with no phase changes of the wave propagation inside the materials have received tremendous attention due to the fascinating physics and potential applications. However, due to the requirement of the degeneracy of dipolar and monopolar resonances and the available resonance-induced losses, the realization of highly efficient and broadband near-zero index metamaterials is still facing challenges. Here we report that by coupling two identical Helmholtz resonators with a connecting channel, acoustic DZIM can be realized. Owing to the presence of a connecting tube, the system can generate the dipolar mode that is independently tunable and the monopolar mode that is virtually unchanged. It thereby makes the mass density (ρ) and the reciprocal of the bulk modulus (1/B) simultaneously crossing zero possible. We numerically obtain the transmission and phase, and then calculate the effective mass density and bulk modulus, which agree remarkably well with the experimental results. Finally, we successfully cloak a rectangle block inside a two-dimensional waveguide grafted by the designed acoustic DZIM array of unit cells. A broadband cloaking is experimentally demonstrated at 1865–1925 Hz, which can offer potential possibilities for vast practical applications.

Using the Design Environment for Low-amplitude Thermoacoustic Energy Conversion in the Classroom.

The Design Environment for Low-amplitude Thermoacoustics Energy Conversion (DeltaEC) is a free software package that is capable of modeling quasi-one-dimensional, multi-domain acoustical networks and includes a 300-page users' guide. The program is a versatile differential equation solver that analyzes a series of "segments" representing ducts, compliances, speakers, etc., that are specified using MKS units. DeltaEC can be a useful pedagogical tool for an introductory course on acoustics in fluids. Examples of its instructional applications include illustration of effective length and quality factor for a Helmholtz resonator and the modes of coupled Helmholtz resonators, as well as standing waves within a resonator of variable cross section and within a catenoidal horn driven by an electrodynamic loudspeaker. Segments representing electrodynamic loudspeakers, radiation loading, and flow resistance in porous media will be used to demonstrate the coupled-oscillatory behavior of a bass-reflex enclosure's complex electrical impedance versus frequency. DeltaEC's plotting features allow immediate visualization of the pressure and velocity fields as well as the power flow or temperature distribution through a network or within a resonator, horn, or waveguide. The "thermo-physical property" feature provides fluid and solid properties at the students' choice of pressure, temperature, and frequency, making it useful as a "handbook" for other assignments.

Experimental Dispersion identification using a fitted state-space model

An identification method that can estimate the dispersion relation of waveguides experimentally using an efficient and accurate procedure is presented. The method fits a linear state-space model before resorting to a kinematic wave model in the frequency region near the pre-identified natural frequencies. The eigenvectors, or mode-shapes, are computed at the sensor locations, and based on the reduced-Bloch mode expansion method, the propagation modes are fitted to match the identified vibration mode-shape at these frequencies. Classical methods to identify the dispersion relation from measured data can be computationally expensive and time-consuming, with limited accuracy in cases of multimode propagation. Results show that the fitted dynamic model expands the frequency range of obtained dispersion curves and enhances the speed of computation and accuracy. The method is derived and verified for both lumped and distributed systems, using numerical finite element simulation. Experimental verification is carried out on two acoustical waveguides. The first is a circular ring-shaped array of coupled Helmholtz resonators, modeled using a lumped parameter model. The second is an air-filled acoustic wave-tube that is modeled as a distributed acoustic-elastic coupled waveguide. The method's strengths and weaknesses are discussed from the experimentally obtained dispersion curves, and its main feature, the ability to fit the dispersion model of weak modes, is highlighted.

Broadband noise mitigation using coupled Helmholtz resonators: a numerical study

In this work we investigate a periodic structure in the frequency range from 20 Hz to 5500 Hz designed for broadband noise insulation. The considered unit cell consists of a simple structure: a pair of polymer pipes with slits carved along the axes, representing two coupled Helmholtz resonators. In order to develop a design with a broad band gap, we analyze the eigenmodes of the infinite two-dimensional structure considering their symmetry and interaction. This analysis is supported by parametric optimization of the resonator geometry. The obtained band diagram is compared with numerically determined transmission coefficient of a finite structure based on the same unit cell. The number of unit cells of the finite structure is chosen to be sufficient for demonstration of insulating properties and stop band formation. Furthermore, we analyze how the transmission coefficient is linked to the pressure field distribution inside the resonators. Owing to the simplicity of the geometry, the obtained results may become a basis for development of budget-friendly passive systems for broadband noise insulation within the audible range of frequencies.

Absorption Mechanism and Optimization of a Subwavelength Acoustic Absorber

A subwavelength acoustic absorber based on parallel coupled Helmholtz resonators is designed to extend the absorption band, where the lateral space is used and verified to reduce the overall thickness. Both theoretical analysis and finite element method are used to demonstrate the low frequency absorption performance. The ratio of absorber thickness to resonant wavelength acquires only 1.87%. It has found that the side location of perforation can move the absorption peak to lower frequency range. The absorption mechanism is investigated by analysing reflection coefficient in the complex frequency plane. The energy dissipation modes underlying absorption performance are further revealed by the viscous energy dissipation patterns. Finally, the absorber is optimized by a DE algorithm to extend the absorption band below 500Hz. The present design offers us an acoustic absorber with excellent stiffness and strength for low-frequency absorption.