Two-dimensional Acoustic Waveguide Research Articles

Acoustic cloning

Cloning refers to producing copies of objects that cannot be distinguished from the original based on their behavior or response. Here, we present a general methodology to clone objects that scatter acoustic waves and demonstrate it experimentally. We acquire digital twins and bring them back to life—a simple two-step process. First, we place the scattering object in a circular receiver aperture and insonify it from the outside using simple speakers. From the recorded data, which may be reverberative, we retrieve the object's scattering Green's functions for radiation conditions using a technique called multi-dimensional deconvolution. This process recovers the temporal and spatial bandwidth and removes the scattering interactions with the boundaries of the experimentation domain, if present. In the second step, the acoustic scatterer is removed and reconstructed holographically using the acquired scattering Green's functions. The hologram scatters arbitrary incident wavefields in real-time exactly like the original object. Low-latency feedback enables reproducing all orders of wave interactions between physical scatterers and the numerical hologram. The two-step process is demonstrated by cloning several rigid scatterers in a two-dimensional acoustic waveguide. Applications range from fully realistic digital scattering models to efficient meta-material experimentation. [Work supported by SNSF grant 197182.]

Topology optimization of array of split-ring resonators in two-dimensional acoustic waveguide for low-frequency transmission problems

This work focuses on the topology optimization of an array of split-ring resonators to achieve nearly zero transmission in the low-frequency regime ranging from 500 Hz to 1000 Hz in 2D waveguide, under the condition of normal-incident plane wave and based on a homogenization scheme known as the Effective Medium Approach (EMA). The EMA transforms each individual resonator defined by its outer radius (rout), neck thickness (h), and the slit width (d), into a homogenous medium characterized by frequency-dependent physical parameters. The transmission coefficient (Tcoeff) of the array can thus be easily evaluated without relying on computationally expensive Finite Element (FE) software. Two optimization algorithms, namely “Sequential Quadratic Programming (SQP)” and “Genetic Algorithm (GA),” have been implemented to the abovementioned topological parameters with sum of Tcoeff being the objective function to minimize. Accuracy of the results has also been validated using software COMSOL Multiphysics® and the satisfactory level of accuracy has proven this approach to be a more efficient and time-saving method to conduct topology optimization of split-ring resonators in low-frequency regime. Moreover, it is noteworthy that the optimized dimensions of resonators are over 20 times smaller than the wavelength in the low frequency range where almost-zero transmission is achieved.

Real-time-controlled artificial quiet channel for acoustic cloaking under varying detection conditions

We consider the problem of hiding non-stationary objects from acoustic detection in a two-dimensional environment, where both the object’s impedance and the properties of the detection signal may vary during operation. The detection signal is assumed to be an acoustic beam created by an array of emitters, which scans the area at different angles and different frequencies. We propose an active control-based solution that creates an effective moving dead zone around the object, and results in an artificial quiet channel for the object to pass through undetected. The control principle is based on mid-domain generation of near uni-directional beams using only monopole actuators. Based on real-time response prediction, these beams open and close the dead zone with a minimal perturbation backwards, which is crucial due to detector observers being located on both sides of the object’s route. The back action wave determines the cloak efficiency, and is traded-off with the control effort; the higher is the effort the quieter is the cloaking channel. We validate our control algorithm via numerical simulations in a two-dimensional acoustic waveguide, testing variation in frequency and incidence angle of the detection source. Our cloak successfully intercepts the source by steering the control beams and adjusting their wavelength accordingly.

Two-Dimensional Distributed Transmission-Line Models for Broadband Full-Tensor Anisotropic Acoustic Metamaterials Based on Transformation Acoustics

We propose the design method for broadband acoustic metamaterials based on the concept of transformation acoustics. Two-dimensional distributed transmission-line (TL) models for full-tensor anisotropic electromagnetic metamaterials are applied to full-tensor anisotropic acoustic metamaterials and the design formulas are shown to uniquely determine the structural parameters of the unit cells. Two-dimensional acoustic waveguide unit cell structures for realizing the TL models are proposed and an acoustic carpet cloak and an acoustic illusion medium are designed according to the introduced theory. The complex sound pressure distributions in the acoustic waveguides of the unit cells are calculated by full-wave simulations to verify the validity of the proposed method, and the broadband operations of the designed carpet cloak and illusion medium are confirmed from the results.

Acoustic analog of twisted bilayer graphene

The emergence of twistronics in bilayer graphene has inspired the creation of new phononic structures that translate quantum effects into macro systems. Here, we introduce an acoustic analog of twisted bilayer graphene that is built with 3D-printed star arrays confined in a two-dimensional acoustic waveguide. The lattices on the top and bottom of the waveguide are coupled by spoof surface acoustic waves. Like its quantum counterpart, the twisting angle of the structure influences wave propagation within the system and its resulting band structures. In analytical models, full-wave simulations, and experiments, we observe mode localization at magic twisting angle that hosts the flat bands. We also study other twisted bilayers with different twisting angles to compare with the magic-angle results. The observation of unusual twistronics effects in acoustic systems demonstrates the potential to identify new quantum materials with simplified acoustic models.

Closed-aperture unbounded acoustics experimentation using multidimensional deconvolution.

In physical acoustic laboratories, wave propagation experiments often suffer from unwanted reflections at the boundaries of the experimental setup. We propose using multidimensional deconvolution (MDD) to post-process recorded experimental data such that the scattering imprint related to the domain boundary is completely removed and only the Green's functions associated with a scattering object of interest are obtained. The application of the MDD method requires in/out wavefield separation of data recorded along a closed surface surrounding the object of interest, and we propose a decomposition method to separate such data for arbitrary curved surfaces. The MDD results consist of the Green's functions between any pair of points on the closed recording surface, fully sampling the scattered field. We apply the MDD algorithm to post-process laboratory data acquired in a two-dimensional acoustic waveguide to characterize the wavefield scattering related to a rigid steel block while removing the scattering imprint of the domain boundary. The experimental results are validated with synthetic simulations, corroborating that MDD is an effective and general method to obtain the experimentally desired Green's functions for arbitrary inhomogeneous scatterers.

Design of highly-efficient acoustic waveguide couplers using impedance-tunable transformation acoustics

In this paper, the theory of impedance-tunable transformation acoustics in the geometric-acoustics limit is proposed to design efficient two-dimensional acoustic waveguide couplers. By choosing suitable impedance functions in the original space, impedance matching between the transformation medium and the background medium becomes possible, and the reflection at the boundary is reduced. The theory can be used to enable efficient acoustic coupling between waveguides of different sizes and different embedded media. By selecting an appropriate impedance function and a tunable acoustic refractive index, the transformed medium in the coupler can become a simplified parameter medium, for which the bulk modulus is a constant. This makes the experiment substantially easier. The problem of a reduced coupling-efficiency at low frequencies (a deviation from the geometric acoustic approximation) can be mitigated by selecting a large acoustic refractive index. Our two-dimensional numerical simulations indicate that this theoretical design works very well. The method can be extended to other transformation acoustic designs including three-dimensional cases.

Immersive wave propagation experiments in a two-dimensional acoustic waveguide

The physical implementation of immersive boundary conditions (IBCs) allows acoustic or elastic waves to propagate seamlessly between a physical domain, such as a wave propagation laboratory, and a numerical simulation virtually enclosing the physical domain. IBCs correctly account for all wavefield interactions between both domains, including higher-order long-range scattering. In this contribution, IBCs are physically implemented in a two-dimensional (2-D) acoustic waveguide. The boundary surrounding the waveguide is densely populated with hundreds of loudspeakers that apply the necessary boundary conditions. The required signals to be injected at the boundary are predicted in real-time by (1) measuring the pressure field and its gradient on two acoustically transparent auxiliary surfaces of microphones inside the waveguide and (2) extrapolating the wavefields to the boundary by evaluating a Kirchhoff-Helmholtz integral using a low-latency, FPGA-enabled data acquisition, computation and control system. Here, we demonstrate the first real-time, 2-D physical immersive wave propagation experiments. We present the setup, as well as a suite of experiments that demonstrate the ability of IBCs to actively suppress broadband incident fields at the boundary of the waveguide and to correctly reproduce all orders of wavefield scattering between the physical experiment and the numerical simulation.The physical implementation of immersive boundary conditions (IBCs) allows acoustic or elastic waves to propagate seamlessly between a physical domain, such as a wave propagation laboratory, and a numerical simulation virtually enclosing the physical domain. IBCs correctly account for all wavefield interactions between both domains, including higher-order long-range scattering. In this contribution, IBCs are physically implemented in a two-dimensional (2-D) acoustic waveguide. The boundary surrounding the waveguide is densely populated with hundreds of loudspeakers that apply the necessary boundary conditions. The required signals to be injected at the boundary are predicted in real-time by (1) measuring the pressure field and its gradient on two acoustically transparent auxiliary surfaces of microphones inside the waveguide and (2) extrapolating the wavefields to the boundary by evaluating a Kirchhoff-Helmholtz integral using a low-latency, FPGA-enabled data acquisition, computation and control system. H...

Wave trapping in a two-dimensional sound-soft or sound-hard acoustic waveguide of slowly-varying width

In this paper we derive novel approximations to trapped waves in a two-dimensional acoustic waveguide whose walls vary slowly along the guide, and at which either Dirichlet (sound-soft) or Neumann (sound-hard) conditions are imposed. The guide contains a single smoothly bulging region of arbitrary amplitude, but is otherwise straight, and the modes are trapped within this localised increase in width.Using a similar approach to that in Rienstra (2003) [13], a WKBJ-type expansion yields an approximate expression for the modes which can be present, which display either propagating or evanescent behaviour; matched asymptotic expansions are then used to derive connection formulae which bridge the gap across the cut-off between propagating and evanescent solutions in a tapering waveguide. A uniform expansion is then determined, and it is shown that appropriate zeros of this expansion correspond to trapped mode wavenumbers; the trapped modes themselves are then approximated by the uniform expansion. Numerical results determined via a standard iterative method are then compared to results of the full linear problem calculated using a spectral method, and the two are shown to be in excellent agreement, even when ϵ, the parameter characterising the slow variations of the guide’s walls, is relatively large.

Selective focusing on small scatterers in acoustic waveguides using time reversal mirrors

We investigate the acoustic selective focusing properties of time reversal in a two-dimensional acoustic waveguide. A far-field model of the problem is proposed in the time-harmonic case. In order to tackle the question of selective focusing, we derive an asymptotic model for small scatterers. We show that in the framework of this limit problem, approximate eigenvectors of the time reversal operator can be obtained when the number of propagating modes of the waveguide is large enough. This result provides, in particular, a mathematical justification of the selective focusing properties observed experimentally. Some numerical experiments on selective focusing are presented.

Embedded Trapped Modes for Obstacles in Two-Dimensional Waveguides

In this paper we investigate the existence of embedded trapped modes for symmetric obstacles which are placed on the centreline of a two-dimensional acoustic waveguide. Modes are sought which are antisymmetric about the centreline of the channel but which have frequencies that are above the first cut-off for antisymmetric wave propagation down the guide. In the terminology of spectral theory this means that the eigenvalue associated with the trapped mode is embedded in the continuous spectrum of the relevant operator. A numerical procedure based on a boundary integral technique is developed to search for embedded trapped modes for bodies of general shape. In addition two approximate solutions for trapped modes are found;the first is for long plates on the centreline of the channel and the second is for slender bodies which are perturbations of plates perpendicular to the guide walls. It is found that embedded trapped modes do not exist for arbitrary symmetric bodies but if an obstacle is defined by two geometrical parameters then branches of trapped modes may be obtained by varying both of these parameters simultaneously. One such branch is found for a family of ellipses of varying aspect ratio and size. The thin plates which are parallel and perpendicular to the guide walls are found to correspond to the end points of this branch.

Trapped modes in a waveguide with a long obstacle

Consider an infinite two-dimensional acoustic waveguide containing a long rectangular obstacle placed symmetrically with respect to the centreline. We search for trapped modes, i.e. modes of oscillation at particular frequencies which decay down the waveguide. We provide analytic estimates for trapped mode frequencies and prove that the number of trapped modes is asymptotically proportional to the length of the obstacle.

Existence theorems for trapped modes

A two-dimensional acoustic waveguide of infinite extent described by two parallel lines contains an obstruction of fairly general shape which is symmetric about the centreline of the waveguide. It is proved that there exists at least one mode of oscillation, antisymmetric about the centreline, that corresponds to a local oscillation at a particular frequency, in the absence of excitation, which decays with distance down the waveguide away from the obstruction. Mathematically, this trapped mode is related to an eigenvalue of the Laplace operator in the waveguide. The proof makes use of an extension of the idea of the Rayleight quotient to characterize the lowest eigenvalue of a differential operator on an infinite domain.