Acoustic Topology Research Articles

Topology optimization of acoustic systems with a multiconstrained BESO approach

This work details a new acoustic topology optimization methodology with applications on the design of systems composed of rigid and porous materials. The Bi-directional Evolutionary Structural Optimization (BESO) algorithm is combined with the Virtual Temperature Method to minimize the occurrence of air cavities and rough surfaces inside rigid and porous domains, hence configuring a multiconstrained optimization approach. The modeling of porous materials is done by the Johnson–Champoux–Allard (JCA) formulation, while the Finite Element Method is used to approximate the governing equations of the physical system. Two different optimization problems are considered separately: first, a rigid–acoustic metasurface is optimized to reduce regional sound pressure levels (SPL) in a set of observed frequencies, while also considering wind permeability through the structure. Secondly, a coupled poro-acoustic absorptive system is treated in order to enhance the sound absorption coefficient in the low frequency range. Both problems are systematized by the implementation of acoustic–rigid and acoustic–porous material interpolation schemes, respectively. The effectiveness of the proposed approach is explored through numerical examples. Here, it is remarked that the methodology maintains the uniformity of rigid barriers, by guaranteeing the absence of internal holes to them. In addition, well-defined cavities are formed in porous domains, increasing their absorption coefficients, but without inflicting macroscopic closed spaces within such structures. In these cases, comparison with appropriate literature is also provided. • Multiconstrained topology optimization algorithm for acoustic problems. • Implementation of the Virtual Temperature Method for connectivity. • Optimization of metasurfaces for reduction of sound pressure levels. • Optimization of porous structures for enhancements of sound absorption coefficient.

Acoustic topology optimization using moving morphable components in neural network-based design

Acoustic topology optimization using moving morphable components in neural network-based design

Measuring and Characterizing the Noise Emission of a Small Combustion Engine after Acoustical Topology Optimization of the Muffler

Measuring and Characterizing the Noise Emission of a Small Combustion Engine after Acoustical Topology Optimization of the Muffler

Acoustic higher-order topology derived from first-order with built-in Zeeman-like fields

Higher-order topological insulators (HOTIs), with topological corner or hinge states, have emerged as a thriving topic in the field of topological physics. However, few connections have been found for HOTIs with well-explored first-order topological insulators. Recently a proposal asserted that a significant bridge can be established between the HOTIs and Z2 topological insulators. When subjected to an in-plane Zeeman field, corner states, the signature of the HOTIs, can be induced in a Z2 topological insulator. Such Zeeman fields can be produced, for example, by the ferromagnetic proximity effect or magnetic atom doping, which drastically increases the experimental complexity. Here, we show that a phononic crystal, designed as a bilayer of coupled acoustic cavities, exactly hosts the Kane-Mele model with built-in in-plane Zeeman fields. The helical edge states along the zigzag edges are gapped, and the corner states, localized spatially at the corners of the samples, appear in the gap. This verifies the Zeeman field induced higher-order topology. We further demonstrate the intriguing contrast properties of the corner states at the outer and inner corners in a hexagonal ring-shaped sample.

Resonant-scattering hybrid device for multiband acoustic topology valley transmission

This paper proposes a hybrid resonant-scattering device combining local resonance and Bragg scattering to achieve simultaneous topological valley-state transport in multiple frequency bands. This acoustic structure was obtained by integrating two types of Helmholtz resonators arranged in a triangular lattice pattern in an air environment. The Dirac point frequency was dominated by the combined strength of resonance and Bragg scattering, presenting a dynamic change process, according to which four designable Dirac points were obtained at frequencies below 14 kHz. Four independently designed and regulated acoustic topological valley transports appeared along the interface separating the topologically diverse sonic crystals after introducing a rotating-scatterer mechanism, as demonstrated by the numerical calculations and experimental results. In addition, since the valley edge states located in the separated edge bands caused by combining resonance and Bragg scattering were interface dependent, a right-hand rule was proposed to evaluate the interface type. This study paves the way for the engineering application of multiband acoustic antennas, acoustic logic control, and other multifunctional acoustic devices.

Synthesis and design of filters and multiplexers with acoustic transversal topology

AbstractThe novel acoustic transversal topology has demonstrated to be a potential candidate for the development of the next generation of communication filters. The major asset of this topology is its capacity to achieve any filter response without the detriment of limited electro-acoustic coupling. Additionally, this topology prompts for an easy connection of different filters to create multiband and multiplexing responses. This study recalls and further details on the design of multiplexers based on transversal topology using bulk acoustic wave (BAW) or surface acoustic wave (SAW) resonators. An important practical aspect of this topology is the need of a BALUN stage at one port of the filter.The use of the transversal topology is then applied to another type of acoustic resonator configuration, coupled resonator filter (CRF). Such a resonator configuration offers control over the phase of each transversal path, allowing us to eliminate the BALUN stage. CRF resonators are modeled by means of a different circuit model than BAW or SAW, which calls for a new synthesis procedure. This paper describes the synthesis approach and circuit transformation for the development of multiplexers based on the transversal arrangement of the CRF resonators. An example of a fully simulated 9-plexer is provided to verify this procedure.

Analytical and numerical modeling, sensitivity analysis, and multi-objective optimization of the acoustic performance of the herschel-quincke tube

This study presents the assessments of the acoustic performance of a Herschel-Quincke (HQ) tube, which includes sensitivity analysis and multi-objective optimization of its design variables. A proper model introduced using the flow characteristics of the HQ tube. Input variables were frequency (f), temperature (T), the ratio of areas (R), and tube length (L). These variables were chosen to be varied in a specified range to best characterize the exhaust flow in internal combustion engines. Then a proper multi-objective genetic algorithm (MOGA) was developed for the acoustic performance and geometry optimization of a two-duct HQ tube; the objectives were maximizing the transmission loss (TL) and at the same time minimizing the backpressure (BP). Besides, the local sensitivity analysis using numerical derivative and variance-based global sensitivity analysis (GSA) using Monte Carlo sampling was performed for the analytical model of the HQ tube. The results showed that the length of the bypass tube is a crucial factor for the maximum sensitivity index (SI) of the TL, while the SI of the BP was maximum for the ratio of areas. The proposed analytical model was proved to be reliable for the TL, showing low values of the error of the sensitivity index (eSI) and less reliable for the BP parameter, showing higher eSI values. For the evaluation of the TL sensitivity, Monte Carlo sampling is relatively inaccurate in the small sample size of 200. It was also observed that the Uniform distribution had lower eSI in lower sample sizes; however, Sobol sampling showed better performance in higher sample sizes. The MOGA optimization proved to be successful in maximizing the TL for the frequencies between 105.84 and 1981.11 Hz, with the TL greater than 20 dB, and the BP less than 0.1. The most efficient solution among the Pareto set after a tradeoff was at 105.84 Hz, for which the TL and the BP were 36.47 dB and 1.50E−02, respectively. The model with the best goodness of fit to represent the Pareto front was the power model with two terms. Then, the acoustic performance of the optimized geometry was investigated using computational aeroacoustics (CAA) in the presence of mean flow in Fluent software. Using the CAA approach, the maximum TL value was obtained for 104 0.4 Hz as 12.14 dB. The simulated TL by CAA had more broadband behaviors with fewer peaks than the analytical approach. The results of this study demonstrated the remarkable potential of the MOGA optimization and sensitivity analysis for acoustic performance and topology optimization for possible applications in internal combustion engines.

Fictitious domain models for topology optimization of time-harmonic problems

A new fictitious domain model for topology optimization of time-harmonic problems based on a wave to diffusion equation transition is proposed. By employing negative values of appropriate material coefficients, a tuneable exponential decay of the field amplitude in the fictitious domains can be obtained, whereas for the conventional model a finite field amplitude is always present. To demonstrate the applicability of the model, we consider two topology optimization problems; a volume minimization problem for acoustic topology optimization for which intuitive meaningful designs are obtained with the proposed model unlike the case with a conventional contrast model. For a structural topology optimization example, the proposed model is shown to remove problematic issues with structural artifacts found for a certain dynamic compliance minimization problem.

Reliability-based acoustical topology optimization of mufflers under noise frequency and temperature uncertainties

A reliability-based topology optimization method is proposed to optimally design mufflers under noise frequency and temperature uncertainties. The optimal mufflers designed with deterministic noise frequency and temperature frequently fail to reduce duct noise effectively when the noise frequency or temperature varies. To resolve this problem, a reliability-based acoustical topology optimization problem is formulated for a two-dimensional expansion chamber muffler. The partition volume inside the muffler is selected as the objective function, and its acoustical reliability and transmission loss are used as constraints so as to design a simple but highly reliable muffler. To expedite finding an optimal solution, a gradient-based optimizer is used; further, to calculate the acoustical reliability and its sensitivity, the first-order reliability method and the weighted uniform sampling method are selectively employed. The formulated design problem is solved for various design conditions, and the acoustical reliabilities of optimal mufflers designed according to the proposed method and the deterministic muffler method are compared. Finally, the noise attenuation performance of the optimally designed muffler is experimentally validated.

Efficient Acoustic Topology Optimization Using Vibro-Acoustic Coupled Craig–Bampton Mode Synthesis

Continuum topology optimization is an effective way to reduce vibration and noise of vibro-acoustic coupling system. However, the high computation time required for calculating the vibro-acoustic responses during topology optimization is a major obstacle for practical applications. In this paper, a novel symmetric method of vibro-acoustic system matrix is proposed, and a new model reduction method is developed based on Craig–Bampton mode synthesis method to compute dynamic responses with adequate efficiency and accuracy for topology optimization. The comparison results show that the proposed method substantially reduces the degrees of freedom (DOFs) and calculation time. The response values and eigenfrequencies calculated by the model reduction method are exactly the same as those of the full model. Furthermore, the bidirectional evolutionary structural optimization (BESO) algorithm is applied to solve the problem of minimizing the response of a single frequency and a certain range of frequency excitation at a specified target point. The results show that the optimization algorithm converges fast, the iterative process is robust and the response values of different coupling systems can be reduced to a higher extend, which indicates the applicability of the optimization algorithm.

Higher-Order Topological Spin Hall Effect of SoundSupported by the National Natural Science Foundation of China (Grant Nos. 11675116 and 11904060), the Jiangsu Distinguished Professor Fund, and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

We theoretically propose a reconfigurable two-dimensional (2D) hexagonal sonic crystal with higher-order topology protected by the six-fold, C6, rotation symmetry. The acoustic band gap and band topology can be controlled by rotating the triangular scatterers in each unit cell. In the nontrivial phase, the sonic crystal realizes the topological spin Hall effect in a higher-order fashion: (i) the edge states emerging in the bulk band gap exhibit partial spin-momentum correlation and are gapped due to the reduced spatial symmetry at the edges. (ii) The gapped edge states, on the other hand, stabilize the topological corner states emerging in the edge band gap. The partial spin-momentum correlation is manifested as pseudo-spin-polarization of edge states away from the time-reversal invariant momenta, where the pseudospin is emulated by the acoustic orbital angular momentum. We reveal the underlying topological mechanism using a corner topological index based on the symmetry representation of the acoustic Bloch bands.

Aeroacoustic topology optimization of noise barrier based on Lighthill's acoustic analogy

Topology optimization for the shape of noise barrier taking into account the aeroacoustic sound source is presented based on Lighthill's acoustic analogy approach. In the previous acoustic topology optimization based on the Helmholtz equation, only simple acoustic sound sources were taken into account. To overcome this limitation, the present aeroacoustic topology optimization is performed using Lighthill's equation that represents the sound propagation by an aeroacoustic sound source. In this study, aeroacoustic sound sources are randomly generated through the stochastic noise generation and radiation method. As an interpolation method of material properties by continuous design variables, the linear filter and the sigmoid penalty function are used. The top shape of noise barrier is designed by the optimization examples for various conditions, such as random aeroacoustic sound sources, interpolation methods, and target frequencies.

Acoustic topology optimization of sound absorbing materials directly from subdivision surfaces with isogeometric boundary element methods

This paper presents an acoustic topology optimization approach using isogeometric boundary element methods based on subdivision surfaces to optimize the distribution of sound adsorption materials adhering to structural surfaces. The geometries are constructed from triangular control meshes through Loop subdivision scheme, and the associated Box-spline functions that generate limit smooth subdivision surfaces are employed to discretize the acoustic boundary integral equations. The effect of sound-absorbing materials on the acoustic response is characterized by acoustic impedance boundary conditions. The optimization problem is formulated in the framework of Solid Isotropic Material with Penalization methods and the sound absorption coefficients on elements are selected as design variables. The potential of the proposed topology optimization approach for engineering prototyping is illustrated by numerical examples.

Acoustic model topology optimization for large vocabulary speech recognition

Acoustic model topology selection work in constructing large vocabulary speech recognition systems is being done empirically or heuristically. In this paper, we propose two improved algorithms, which are based on Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) respectively, on the basis of our previously proposed algorithms to select and optimize model topologies for small or medium vocabulary speech recognition systems. Our improved algorithms attain the goal of optimizing acoustic model topologies for large vocabulary speech recognition systems mainly through modifying the encoding schemes of our previously proposed algorithms. Experiments on the dialogue corpus of Inner Mongolia University show that, compared with the conventional acoustic model topology selection method, our newly proposed algorithms are able to bring much higher recognition performance for large vocabulary speech recognition systems by optimizing their acoustic model topologies.

Underwater acoustic metamaterial based on double Dirac cone characteristics in rectangular phononic crystals**Project supported by the National Natural Science Foundation of China (Grant Nos. 11602269, 11972034, and 11802213), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB22040301), and the Research Program of Beijing, China (Grant Nos. Z161100002616034 and Z171100000817010).

We theoretically construct a rectangular phononic crystal (PC) structure surrounded by water with C2v symmetry, and then place a steel rectangular scatterer at each quarter position inside each cell. The final complex crystal has two forms: the vertical type, in which the distance s between the center of the scatterer and its right-angle point is greater than 0.5a, and the transverse type, in which s is smaller than 0.5a (where a is the crystal constant in the x direction). Each rectangular scatterer has three variables: length L, width D, and rotation angle θ around its centroid. We find that, when L and D change and θ is kept at zero, there is always a linear quadruply degenerate state at the corner of the irreducible Brillouin zone. Then, we vary θ and find that the quadruply degenerate point splits into two doubly-degenerate states with odd and even parities. At the same time, the band structure reverses and undergoes a phase change from topologically non-trivial to topologically trivial. Then we construct an acoustic system consisting of a trivial and a non-trivial PC with equal numbers of layers, and calculate the projected band structure. A helical one-way transmission edge state is found in the frequency range of the body band gap. Then, we use the finite-element software Comsol to simulate the unidirectional transmission of this edge state and the backscattering suppression of right-angle, disorder, and cavity defects. This acoustic wave system with rectangular phononic crystal form broadens the scope of acoustic wave topology and provides a platform for easy acoustic operation.

Methods for evaluating in-duct noise attenuation performance in a muffler design problem

In this study, methods for evaluating the noise attenuation performance of a muffler in a muffler design problem are investigated, and a proper evaluation method is suggested for actual noise reduction in a duct when an optimally designed muffler is mounted on a duct. Mathematical expressions of the transmission loss, insertion loss, and level difference for a simple expansion chamber muffler are developed from basic acoustic equations. The effects of the locations of the measurement points, tailpipe length, and impedance at the end of the duct on the noise attenuation performance calculated using the three evaluation methods are discussed. The TL and IL maximization problems formulated using topology optimization are solved for a muffler unit, and the noise attenuation performances of the optimally designed mufflers are compared when mounted on a duct. Another acoustical topology optimization problem, a partition volume minimization problem for a muffler design, is formulated to reduce the in-duct broadband noise, and the noise attenuation performance of the optimal muffler obtained using this formulation is experimentally validated. These research results will contribute to the development of a muffler design method with high accuracy by reducing the discrepancy between the noise attenuation performances of a muffler unit and a muffler mounted on a duct.

Dual-band acoustic topological insulator based on honeycomb lattice sonic crystal

Based on honeycomb-lattice sonic crystals with gear-like scatterers, we study and design a pseudospin-dependent dual-band acoustic topological insulator. Compared with cylindrical scatterers with only a single tunable structure parameter (radius), there exist four tunable parameters for the gear scatterer, which enables the sonic crystal to realize four-fold accidental degeneracy at two different frequencies simultaneously. By changing structure parameters of the gear-like scatterers, we can obtain topological phase transitions between two sonic crystals. Based on this, we design acoustic topological waveguides based on two honeycomb-lattice sonic crystals with different topological phases, and introduce two kinds of defects (a lattice disorder and a bend) into the topological waveguide near the domain wall. Numerical simulations show that pseudospin edge states almost immune to two types of defects and can pass through the topological waveguides with negligible backscatterings. Compared with the results for the topological waveguide without defects, the measured transmission spectra are almost unchanged with the two types of defects, which further experimentally verify the robustness of pseudospin-dependent edge states. Additionally, by keeping the structure of the sonic crystals unchanged, we can also obtain another four-fold accidental degenerate Dirac point and the corresponding topological sound phase transitions in the high-frequency region. The simulations show that there also exists a pair of edge states in the overlapped bulk bandgap of the two sonic crystals in the high-frequency region. It is worth noting that the tiny gap between two edge states is larger than that in the low-frequency region, which may arise from the greater difference between the distributions of pressure eigenfunction of two sonic crystals. The proposed dual-band acoustic topology insulator has potential applications in multi-band sound communication and sound information processing.

Acoustic topology optimization of porous material distribution based on an adjoint variable FMBEM sensitivity analysis

We develop an acoustic topology optimization approach in this work for the surface design of structures covered by porous materials. The fast multipole boundary element method (FMBEM) is employed for the sound scattering analysis. The acoustic absorption characteristics of porous materials are numerically modeled using the Delany–Bazley–Miki empirical model. Based on the solid isotropic material with penalization (SIMP) method, the optimization is performed by setting the artificial element densities of porous material as the design variables, minimizing the sound pressure or the dissipated sound power as the design objective. As a key treatment in this study, we develop a fast sensitivity analysis approach based on an adjoint variable method (AVM) and the fast multipole method (FMM) to calculate the sensitivities of the objective function with respect to a large number of design variables. The FMM is applied to accelerate the vector-matrix product required by the AVM. According to the gradient information, the method of moving asymptotes (MMA) is used for solving the optimization problem to find the optimal solution. We validate the proposed topology optimization approach through numerical examples of acoustic scattering over a single cylinder and multi cylinders, and demonstrate its ability to handle large-scale problems.

Topology optimization of reactive acoustic mufflers using a bi-directional evolutionary optimization method

This article proposes an acoustic muffler design procedure based on finite element models and a Bi-directional Evolutionary Acoustic Topology Optimization. The main goal is to find the best configuration of barriers inside acoustic mufflers used in the automotive industry that reduces sound pressure level in the outlet of the muffler. The acoustic medium is governed by Helmholtz equation and rigid wall boundary conditions are introduced to represent acoustic barriers. The continuum problem is written in the frequency domain and it is discretized using the finite element method. The adopted objective function is Transmission Loss (TL). Increasing TL guarantees that the sound pressure level ratio between outlet and inlet of the muffler is reduced. To find the configuration of acoustic barriers that increases the Transmission Loss function of the muffler an adaptation of the Bi-directional Evolutionary Structural Optimization (BESO) method is used. Applying the proposed design procedure topologies in 2D models are reached, which raises the Transmission Loss function for one or multiple frequencies. Three examples are presented to show the efficiency of the proposed procedure.

An isogeometric approach of two dimensional acoustic design sensitivity analysis and topology optimization analysis for absorbing material distribution

A study of structural shape optimization and absorbing material distribution optimization of noise barrier structures based on the recently proposed isogeometric analysis method with exact geometric definitions is presented. The acoustic scattering is approximated using the basis functions that represent the geometry. A fast multipole method is applied to accelerate the solution of the boundary element method (BEM). The Burton–Miller formulation is used to overcome the fictitious frequency problem when a single Helmholtz boundary integral equation is used for the exterior boundary–value problem. The strongly singular integrals in the Burton–Miller formulation using the isogeometric BEM are evaluated explicitly and directly, particularly for the sensitivity formulation with a hyper-singular integral. The optimality criteria method is used for two types of optimization analyses, shape optimization and material distribution topology optimization. For the shape optimization, the design variables can be set to the locations of the control points because the control points determine the shape of structure. For the second optimization, a new material interpolation scheme for acoustic problems based on the solid isotropic material with penalization (SIMP) method is given, where the interpolation variable is not the real structural density used in a conventional SIMP, but a fictitious material density that determines the normalized surface admittance. Several examples are presented to demonstrate the validity and efficiency of the proposed algorithm.