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Scientific Reports volume 14, Article number: 24011 (2024 ) Cite this article Angled Noise Barrier
Active acoustic metamaterials (AAMM) have garnered special attention because of their potential as multi-function devices. In this direction, the present article demonstrates a novel AAMM that can be programmed as a multi-functional Active Acoustic Meta-device (AAMD) that can switch functionalities between Acoustic Switch (AS), Acoustic Lens (AL), and Acoustic Barrier (AB). Functionality: AL corresponds to the wave vector space, and AS and AB correspond to the frequency space of the proposed AAMM. Additional functionality, such as acoustic logic gates in phase space, is also envisaged. The proposed design is found to change the dispersion diagram by acquiring different configurations while keeping the basic design parameters constant. These design parameters include constituent elements, lattice constants, and filling fractions. Further, for the said functionalities, the proposed AAMM does not rely on the deformation characteristics of the constituents. It rather capitalises on the possible relative displacements of the scatterers. As an AL, AAMM demonstrates zero angle refraction, i.e., collimation, and negative refraction of the transmitted beam at a given angle of incidence over a frequency range of 200 kHz (22.22% of the applied frequency sweep, a.f.s.). AB is shown to attenuate acoustic energy over a frequency range of 700 kHz (77.78% of a.f.s.) compared to its reference and foundation design, a statically designed Phononic Crystal (PnC). Furthermore, as AS, it operates over the entire range of applied frequency sweep (100 kHz to 1000 kHz), i.e., over the frequency range of 900 kHz (100% of a.f.s.).
Acoustic Meta-material (AMM)s1,2,3 in general are composites that manipulate the acoustic waves in unprecedented ways compared to the naturally available materials4,5,6,7. Manipulation of the acoustic wave depends on (i) the periodicity of the dispersed phase (s) in a matrix phase4,5,6,7; (ii) the contrast in physical properties of the constituents of the composite, e.g., speeds of sound and density between the dispersed and the matrix phase8; (iii) sufficient filling fraction of the dispersed and the matrix phase8; and (iv) the geometry of the unit cell6. In principle, these features of such composites help utilize the principles of Bragg’s scattering4,5,6,7 and or local resonances2,9,10 to manipulate the acoustic waves in an exotic manner.
Due to their unique characteristics, Meta-material (MM)s open the avenues for the realization of the diverse unprecedented applications. Among such unique characteristics, their ability to exhibit fractional and negative index of refraction has spurred a great deal of interest. Accordingly, they are explored both theoretically11,12,13,14,15,16,17,18 and experimentally19,20,21,22,23,24 in various studies. During their evolution, such materials in photonic domain were characterized by super-prism12, super-refraction13 and perfect lens14 phenomenon. In acoustic domain, these unusual refractions have demonstrated acoustic imaging20,21,22,23,24,25, sub-wavelength resolutions in medical applications26, pulse decomposition in acoustic signal processing27, acoustic focusing19,22,23,24,25,26,27, self-collimation16,28,29,30,31, cloaking32, communication in acoustic domain33, multi-function33 and multi-refringences24.
Among these refractions, the present work explored the multi-refringences due to their vast potential applications ranging from materials microscopy to medical microscopy, for example. Multi-refringences depend on the Equi-frequency Contours (EFC)s of the transmission band and are, hence, a strong function of the anomalous dispersion of the Bloch modes16,17,18,19,20,21,22,23,24,27,29,30,31,33,34. However, the reasons for such dispersion bands may be: (1) the introduction of defects24,33 and or cavities34; (2) a multi-frequency source34,35; (3) exciting both longitudinal and transverse modes, e.g., phononic crystals33; and (4) normal defect-free phononic24 or sonic21 crystals that shift EFCs away from the centre of the Brillouin zone.
This article intends to demonstrate the unprecedented control of the multi-refringences through a novel AAMM used to develop the multi-functional AAMD. The AAMM is developed from the normal PnC demonstrated in recent literature. Both AAMMs and their explored applications are novel. AAMM is novel in its design and application for its active control of the multi-refringences with substantial independence of the incidence angle and frequency of the incident wave.
In beginning of the article, the experimental results of the reference literature are validated through a computational model considering the design parameters of the unit cell of the PnC used in the said reference. Then, an extended study to numerically demonstrate the controlled programmable multi-refringences through the proposed AAMM is conducted. Finally, such demonstration is considered as sufficient evidence to validate the practicality of a multi-functional AAMD.
Most of the designs in AMMs are static in nature. Once the elements of the composites are tuned for their properties and design, i.e., the shape and material of the scatterer and their relative positioning in the periodic structure is defined, their dynamic response, i.e., the interaction between the interacting waves and structures, is static in nature. Such designs, once developed, are limited to the achieved static wave characteristics, e.g., their constant dispersion diagram for the targeted frequency ranges. This limitation is due to their static design. Accordingly, researchers successfully explored the possibility of active designs. Most of these designs utilized the electrical control of the piezoelectric transducers8,36,37,38,39,40,41 whereas many used mechanical energy for the active response42,43,44,45,46,47,48. Some used electromagnetic forces to achieve AAMM49,50,51,52. Others investigated various multidisciplinary approaches in developing AAMM53,54,55,56,57,58.
After reviewing the AAMM substantially, the major hurdles in their evolution were found to be: (a) static design; (b) prime dependence on local resonances. Reliance on resonances implies frequency dispersions (dependence) and narrow frequency bands in the effectiveness of AMM59,60,61,62; (c) limited deformation characteristics of the re-configurable AAMM; (d) sophisticated design of the powered devices.
Accordingly, a novel AAMM that achieves controlled configurations (setups) through substantial relative movements of the denser phases that are typically called scatterers is developed. Further, with such movements, the proposed AAMM maintains the periodicity of the scatterers in the matrix.
Owing to the research gaps in the existing field, the possibility of significant relative motions of the scatterers in a particular class of Sonic crystals (SC)s, PnCs, AMMs, and even for other AAMMs that use fluid as matrix material has not yet been investigated. Such a possibility is successfully explored for statically designed PnC of the said reference work that uses water as a fluid for the matrix material. The developed AAMM is a two-phase system, i.e., with the core material and water only. No conventional approaches to local resonances, i.e., the use of softer materials or Helmholtz resonators, are integrated into the design. Further, it is more fascinating as multi-functionality is demonstrated using a simple axisymmetric shape of the scatterer, i.e., cylindrical scatterers.
For the experimental validation of the numerical model of the proposed AAMM, the reference chosen from the recent literature is the work of Jin et al.24.
As stated earlier, the design parameters of the unit cell of the said reference work is adopted to develop an AAMM. As shown in the Fig. 1, the scatterer of the reference work is split into four equal segments (quadrants). These segments can have relative radial and angular displacements about the centre of the unit cell.
Design comparison. Figure (A) shows the developed AAMM design, and Figure (B) shows the reference design. Unit cell and scatter sizes remain the same in the two designs.
These displacements can be mechanized and programmed against the desired frequencies as shown in Fig. 2. This figure demonstrate the functioning of a unit cell of proposed active acoustic meta-device AAMD.
Exploded view of the unit cell of the proposed AAMD. An inset image at right top to this figure shows the actual unit cell of the said AAMD.
Through component 1.1, component 1.2 rests on component 1.4, relative to which it moves linearly along its guides. 1.1 through the guides of 1.4 operate in the spiral slots of 1.6, which are coupled to the actuator 1.3. Accordingly, components 1.1, 1.2, 1.4, and 1.6 operate through 1.3, which results in radial movements of 1.2. Further, 1.3 rests on 1.5, which is rotated through 1.8 by actuator 1.7. 1.7 is fixed to the ground, and through 1.9, the motion of 1.10 and 1.5 results. Therefore, this mechanism results in the radial and angular displacements of the scatterers (1.2).
Degree of tuning: The above design reveals that the scatterer’s individual quarter segment has two degrees of freedom (DOF): radial and angular. Since all four quarter segments are synched together, there are only two DOFs for the whole unit cell. The degree of tuning for the radial DOF varies from 0 to (a–d)/2, and the degree of tuning for the angular DOF varies from 0 to 45 deg. The step size depends on the computational and experimental resources available. In the present work, for the available resources, four radial and four angular steps are considered.
The investigation is performed in two stages: (1) Experimental validation of the numerical model of the proposed design; and (2) Extension study of the validated numerical model to demonstrate multi-refringence.
The design parameters of the referred PnC are shown in Fig. 1. The said work used the Plane Wave Expansion Method (PWEM) for the EFCs and band structure calculations. In addition, the numerical simulations of the acoustic transmission were performed using COMSOL Multiphysics. The Table 1 shows the acoustic properties of the constituent elements of the PnC and AAMM.
EFCs depend entirely on the band structure diagram. For AAMM, the band structure calculations are performed using Finite Element Method (FEM)-based tool COMSOL Multiphysics. The comparative results of dispersion diagrams for the two cases are shown in Fig. 3. There are some deviations in the numerical results of the two approaches, PWEM and FEM (used in COMSOL Multiphysics). This is significant for the second and third pass-bands. However, the patterns followed in both cases are the same. Accordingly, a convergence study for FEM based numerical results is performed. The calculations are repeated while considering the standard convention on the size of the elements to resolve the propagating acoustic wave, i.e., l/5 for the maximum size of the element and l/10 for the minimum, which results in substantially lower number of elements comparing the one used in the previous results. Both the results converged well, as shown in the Fig. 3B.
Dispersion and convergence diagrams. Figure (A) shows the comparative results of the dispersion diagram for PWEM24 and FEM followed in the present work. Figure (B) shows the convergence study for the FEM results.
Following the reference work, the experimental set-up for the numerical modeling to simulate transmission across the AAMM is shown in the Fig. 4.
Experimental set-up for the transmission simulations across the AAMM.
The unit cell configuration of the reference design is one of the reconfigurable configurations attained by the proposed AAMM, i.e., when the radial displacement between scatterer segments is zero; refer to Fig. 2. Further, the acoustic responses of the said configuration of the reference are experimentally supported. The simulation results of the Sound Pressure-intensity Level (SPL) for the AAMM are substantially in sync with the experimental results of the cited literature. Therefore, the numerical model of the AAMM is experimentally validated. Further, these results of the AAMM are well supported by the corresponding Wave Vector Diagram (WVD)s, refer to Supplementary Note 1.
The main study emphasized here is the possible dynamic control of the multi-refringences that lack parallel experimental backing. Therefore, it is crucial to have some sound alternative interpretive tools. WVD formalism13,21,24 is a well-established geometrical tool in this regard. For more details on WVD, refer to Supplementary Note 2.
The preceding section developed substantial confidence in the validity of the methods and approach for the subsequent study, demonstrating multi-refringence control. As stated earlier, all design parameters pertaining to the PnC are retained except that the scatterer is split into four equal segments; refer to Figs. 1 and 2. Further, for the consistency of the comparison, numerical simulations and their geometrical counterparts, i.e., the WVDs are evaluated at the same set of angles of incidence of the source waves as in the cited reference work. Furthermore, the operating frequency is again 570 kHz. These results are shown in Figs. 5 and 8
Considering the key features of the AAMM that are used for multi-refringence control, such a study may further be divided into the following: (1) Effect of the radial displacement on multi-refringence control; and (2) Effect of rotation on multi-refringence control.
Effects of radial displacements at constant rotations, angle of incidence and frequency.
These effects are analyzed at a particular rotation of the scatterers, i.e., rotations are kept constant. Further, supporting WVDs are provided for the peculiar observations only.
Pass-bands intercepted by the operating frequency. Referring to the legends to this figure, suffix (1) and (2) corresponds to the number of such intercepted bands at the operating configuration.
Referring to Fig. 5, the AAMM is capable of producing and controlling the collimated beams for the incidence wave angle between \(0^{\circ }\) and \(10^{\circ }\) . For demonstration of such a case, the incidence angle, \(\theta _{inc}\) as \(0^{\circ }\) and the scatterer rotation, R to be \(0^{\circ }\) as well are selected, refer to corresponding entries in Fig. 5. The steps for the angular displacements of the scatterers are \(15^{\circ }\) and each step of the radial displacement is half of the higher one.
With increasing radial displacement, otherwise diverging beam at the exit of the AAMM starts converging. Such beams are found collimated with radial displacement onwards, where D equal 0.0975 mm, over the entire interfaces of AAMM, except the face receiving the incident beam. However, such beams are evanescent in nature away from the main transmitted collimated beam. At the maximum possible radial displacement value of the AAMM i.e., 0.195 mm, the width of the main beam increases. However, the strength of such a beam faded away from its centre. Further, to the side (lateral) interfaces of the AAMM, the evanescent collimated beams are found almost orthogonal; refer to Fig. 5 (\(\mathrm{R = 0}^{\circ }\) , D = 0.0975 mm, and 0.195 mm). All these configurations are well supported by their geometrical counterparts, wave vector diagrams; refer to Fig. 7. As a special case of collimated beam, consider the \(\theta _{inc}\) as \(10^{\circ }\) at \(\mathrm{R = 0}^{\circ }\) , D = 0.0975 mm, and 0.195 mm. In these configurations, a \(90^{\circ }\) transmitted collimated beam appears to the right of the AAMM.
Collimation study of the transmitted beam, at constant rotation, angle of incidence and frequency.
The main highlight of the present work is the ability of the proposed AAMM to modify the dispersion diagram and hence the EFCs that modify the corresponding transmitted acoustic waves while preserving the passive parameters of the design, e.g., constituent elements, filling fraction, lattice constant, etc.; refer to Fig. 6 and WVDs in Fig. 7.
In Fig. 7, EFCs change with the configurations. It reflects the change in dispersion diagrams. Similar control may be demonstrated for the other classes of multi-refringences; refer to Fig. 5. In general, for the cases \(\theta _{inc}\) onward \(20^{\circ }\) , both negative reflection and refraction coexist with the usual positive reflection and refraction, refer to caption of Fig. 2 of the Supplementary Note 1.
Effect of the rotation at constant radial displacement, angle of incidence and frequency.
These effects again are peculiar at D equal to 0.195 mm; refer to Fig. 8. For collimation, such an effect is demonstrated for \(\theta _{inc}\) at \(0^\circ\) and for multi-refringence at \(\theta _{inc}\) at \(20^\circ\) onward. Collimated beams start diminishing with increasing angle of rotation and are totally lost beyond R equal to \(30^\circ\) ; refer to Fig. 8. WVDs for the configurations, where R equals \(30^\circ\) and onward, demonstrate the existence of the stop band at these configurations. In such WVDs, no Bloch modes are excited at the wave incidence angle of \(0^{\circ }\) . Incident wave vectors sway away from the EFCs.
Pass-bands intercepted by the operating frequency.
Accordingly, following the Eq. (1) Supplementary Note 2 no Bloch waves are excited. This is supported by the existence of the band-gap at operating frequency at such configurations for the normal incidence, i.e., along the \(\Gamma -\) X direction; refer to Fig. 9. Here, the pass-bands for the said configurations are not intercepted by the operating frequency along the \(\Gamma -\) X direction.
As for the preceding case, these results are well supported by the corresponding WVDs; refer to Fig. 10. As a special case of collimated beams, consider the configuration R equals to \(30^\circ\) at \(\theta _{inc}\) to be \(30^\circ\) . Here, the evanescent collimated transmitted beams are almost parallel to the incident beam; refer to Fig. 8.
Figure 9 represents the pass-bands that are intercepted by the operating frequency at the selected configurations of the AAMM. Similar to the preceding study on controlled collimation, the control of other classes of multi-refringence can be demonstrated for \(\theta _{inc}\) at \(20^{\circ }\) onward.
Collimation study of the transmitted beam, at constant radial displacement, angle of incidence and frequency.
Earlier sections revealed some fascinating results, i.e., controlled collimation and negative refraction for the constant passive elements of the design, angle of incidence, and frequency. Actual sound travels at multiple frequencies. Accordingly, for the real-life applications of the findings, a study to explore the frequency dispersion of the said functionalities, i.e., collimation and negative refraction is conducted. The results of the said study can be categorized as follows:
Collimated acoustic beams find numerous practical applications ranging from material microscopy, e.g., Non-Destructive Testing (NDT), to biomedical microscopy, e.g., ultrasounds63. Further, recently, such beams have been successfully explored for the communication and storage of information in the acoustic domain33,34.
Broadband collimation of acoustic beam.
Dispersion diagram for the configuration, D-0.195, \(\mathrm{R-0}^{\circ }\) Data in red shows the limits of the band-gap.
From 600 to 650 kHz, there is a band-gap for the infinite size of the AAMM. As the transmission is shown for the finite size of the AAMM, 600 kHz onwards up to 650 kHz shows the evanescent beams. Collimation started again from 700 to 720 kHz.
Negative refraction in acoustic metamaterials paved the way for acoustic lenses19,22,64,65 imaging20,25 and cloaking32. Through the following study, broadband negative refractions that can be switched between and, as such, are controllable are demonstrated. For the entire range of the reported frequencies, the incidence angle of the beam remains constant at \(30^{\circ }\) . Negative refraction is reported within the AAMM as well as for the transmitted beam. For intra-AAMM negative refraction, refer to the figures in Fig. 13 for the frequency range of 440 to 570 kHz. This phenomenon can be observed through the rightward shift of the transmitted beam across the AAMM. Intra-AAMM negative refraction is also reported for the remaining frequencies in Fig. 13. However, for the quoted range, it is explicit. Negative refraction for the transmitted beam is observed for the frequency range 840 to 970 kHz; refer to Fig. 13. However, here the negative and positive refractions coexist as birefringence.
Considering the outcomes of the various configurations, a double-layered AAMM with the same passive design elements as used in the preceding sections and the reference24 is developed. The size of each layer is 100 \(\times\) 5, such that the net AAMM size remains the same as with previous structures, i.e., 100 \(\times\) 10.
Comparative effect of double layered AAMM.
Effect of double layered AAMM on broadband collimation.
Following the same approach as for the multi-layered AAMM, a multi-layered, multi-segmented AAMM for the same passive design elements is also developed and investigated. Finding, D-0.04875, \(\mathrm{R-0}^{\circ }\) , and D-0.0195, \(\mathrm{R-0}^{\circ }\) , as the key configurations for the collimation, they are used in developing the said AAMM. For the ease of the demonstration, the double-layered AAMM is segmented into three segments. Therefore, in all, six portions composed of two rows (layers) and three columns (segments) of the AAMM can be configured independently; refer to Fig. 16. Column-wise, two segments of the first column were selected as D-0.04875, \(\mathrm{R-0}^{\circ }\) , and the remaining four portions as D-0.0195, \(\mathrm{R-0}^{\circ }\) . For ease of configurations distribution, the size of the AAMM is reduced to 90 \(\times\) 10, such that each portion is composed of 30 \(\times\) 5. The combination of the said configurations are selected because, for the configuration D-0.04875, R-0, some lateral propagation of the beam within the AAMM is observed at frequency 570 kHz and angle of incidence \(10^{\circ }\) onwards, refer to Fig. 5. Further, the majority of the configurations are selected at D-0.0195 and \(\mathrm{R-0}^{\circ }\) to ensure collimation.
Results, multi layered, multi segmented AAMM.
To map the entire surface of the AAMM at the inlet side, the range of the incidence angle is increased, i.e., \(-20^{\circ }\) to \(70^{\circ }\) . As anticipated, all face orthogonal collimation is achieved, i.e., in the range \(-20^{\circ }\) to \(20^{\circ }\) , almost \(90^{\circ }\) -collimated beams at all the exit faces of the AAMM are achieved. Refer to Fig. 16.
Among the various applications, transmission barriers remain the most important application of AMMs. Through the following simulations, a wide-band transmission barrier is demonstrated. Transmission loss for the set-up referred to in Fig. 4 is evaluated for the entire range of the incidence angles, i.e., \(\theta _{inc}\) in the range \(0^{\circ }\) –\(40^{\circ }\) . However, the transmission loss is reported for the discrete angles, i.e., \(0^{\circ }\) , \(10^{\circ }\) , \(20^{\circ }\) , \(30^{\circ }\) , and \(40^{\circ }\) , for which the multi-refringence was reported earlier. The choice of such a selection is only to highlight the multi-functionality of the AAMM over the same sets of parameters.
Transmission loss spectrum of the proposed AAMD. Figure (A) shows the entire range of the transmission loss or transmission that is achievable with various configurations of the AAMD. Figure (B) demonstrates the improvements in transmission loss or transmission comparing PnC. The curve in red shows the prospective domains of the AB. Similarly, the curve in blue shows similar results for the AL, and multicoloured curves in between these domains are the domain of the AS.
Referring to figures in Fig. 17, curves in red and blue demonstrate the multi functional prospective domains of the AAMD, i.e., as a AB and AL, respectively. A threshold value of minimum 10 dB is considered the defining limit between AB and AL66,67. Figure 17A shows the entire range of transmission loss or transmission that is attainable with the various configurations of the AAMD. Figure 17B demonstrates the improvements in transmission loss or transmission compared to PnC of the reference article24. All reported configurations for the collimations and negative refractions are either on or near the blue curve of Fig. 17. Such a curve reports the transmission spectrum of the proposed AAMD. Again, the characteristics of the acoustic barrier are explored for the frequency range 100–1000 kHz, i.e., the range for which multi-refringences are demonstrated. It is strongly believed that the proposed AAMD is capable of achieving ultra-broadband transmission loss, provided a larger frequency sweep is applied. As verified from Fig. 17B, at worst the proposed AAMD performs as a PnC, i.e., the curve in black.
The main highlight of the proposed design is its ability to attain all stated configurations dynamically, i.e., from the PnC to the comparatively complex design of multi-layered and multi-segment AAMM. The proposed AAMM can be dynamically tuned. The step size depends on the computational and experimental resources available. In the present work, for the available resources, four radial and four angular configurations were considered. In the future, more configurations can be considered to get better predictions for intermediate degrees of tuning.
Figures (B) through (F) show the peculiar cases of collimation achieved through AAMM comparing Figure (A) that shows the reference the case for PnC. Similarly, Figures (H) and (G) represents the peculiar case of negative refraction. Figures (I) and (J) compare the best transmission loss profiles over the PnC and AAMM respectively. For negative refraction operating frequency is 550 Hz and for other cases it is 570 Hz.
Further, all reported phenomena are achieved with simple design elements, i.e., a circular scatterer, a square unit cell, and a two-component system (steel and air). AAMM with a two-component system is novel in itself, apart from the other novelties reported. To the best of our knowledge, this is the first time the control of the multi-refringences at a given operating frequency and angle of incidence has been reported. These results are reported over a broader range of frequencies, which increases its potential for real-life applications, whereby, actual sound travels over a range of frequencies rather than at a constant frequency. Furthermore, multiple configurations achievable through the proposed design are independent of scatterer types. Therefore, the advantages of incorporating defects into periodic structures and using different types of scatterers can further be explored.
Figure 18 highlights the key features of the AAMD. These Three Dimensional (3D) surface plots give more insights into the appealed features of the AAMD. As stated earlier, collimated beams have numerous practical applications ranging from material microscopy, e.g., NDT, to biomedical microscopy, e.g., ultrasounds63. Similarly, negative refraction finds applications in acoustic lenses19,22,64,65, imaging20,25 and cloaking32. Through the present article, the tripartite functionality of the AAMD, i.e., the AS, the AL and the AB is successfully demonstrated.
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request. All data generated or analysed during this study are included in this published article.
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Acoustics and Vibration Laboratory, School of Mechanical and Materials Engineering, IIT Mandi, Kamand, Mandi, Himachal Pradesh, 175005, India
Department of Mechanical Engineering, IIT Delhi, Hauz Khas, Delhi, 110016, India
School of Mechanical and Materials Engineering, IIT Mandi, Kamand, Mandi, Himachal Pradesh, 175005, India
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A.P. wrote the main manuscript. Dr. A.G. and Dr. S.N. review the manuscript.
The authors declare no competing interests.
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Pundir, A., Gupta, A. & Nag, S. Multi-functional programmable active acoustic meta-device: acoustic switch, lens, and barrier. Sci Rep 14, 24011 (2024). https://doi.org/10.1038/s41598-024-71737-0
DOI: https://doi.org/10.1038/s41598-024-71737-0
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