Acoustic Boundary Conditions Research Articles

Results on a nonlinear wave equation with acoustic and fractional boundary conditions coupling by logarithmic source and delay terms: Global existence and Asymptotic behavior of solutions

The nonlinear wave equation with acoustic and fractional boundary conditions, coupled with logarithmic source and delay terms, is notable for its capacity to model complex systems, contribute to the advancement of mathematical theory, and exhibit wide-ranging applicability to real-world problems. This paper investigates the global existence and general decay of solutions to a wave equation characterized by the inclusion of logarithmic source and delay terms, governed by both fractional and acoustic boundary conditions. The global existence of solutions is analyzed under various hypotheses, and the general decay behavior is established through the construction and application of a suitable Lyapunov function

Global existence and decay of a viscoelastic wave equation with logarithmic source under acoustic, fractional, and nonlinear delay conditions

This study is concerned with a nonlinear viscoelastic wave equation with logarithmic source term. By considering the nonlinear distributed delay feedback influenced by acoustic and fractional boundary conditions at the boundary coupling, we establish the global existence and general decay results under appropriate assumptions, even in the case of a general kernel. This result extends and complements some previous results.

Neural Impedance Boundary (NeIB): a neural-network based framework for acoustic surface impedance estimation utilizing sparse measurement data

Amidst recent advancements in the 3D digital representation that have significantly enhanced the modeling of geometric attributes of pre-existing environments, accurate estimation of acoustic boundary conditions remains a complex challenge. This paper presents a novel way to determine what we refer to as a neural boundary field, using physics-informed neural networks (PINN). The aim is to estimate the surface impedance measured in-situ by utilizing several points of sound field pressure. This approach couples the Helmholtz equation with automatic differentiation in the PINN framework to estimate accurately the surface impedance using a hybrid modeling approach where measurement data and domain knowledge in the form of equations for the acoustic waves are combined. As a proof-of-concept, we train the neural networks using 2D sound field data obtained from high-fidelity numerical acoustical simulations that incorporate actual surface materials parameters. We discuss the measurement techniques associated with this method and outline our vision for its application to 3D scene reconstructions in the future.

Identification of flame transfer function and mechanism analysis of the influence of boundary impedance characteristics on thermoacoustic instability

Thermoacoustic instability is a common problem in the operation of modern gas turbines. The prediction of thermoacoustic instability and the clarification of its mechanism are the research focus and difficulty in the gas turbine industry. As a response function of flame to acoustic disturbance, flame transfer function is a key parameter in the study of thermoacoustic instability. In this paper, based on the scaled adaptive simulation (SAS) model combined with the eddy dissipation concept (EDC) combustion model, the time-domain flow field data are processed by the system identification method, and the results of flame transfer function extraction are in good agreement with the experimental values. Then, the detailed derivation process of the low-order thermoacoustic network model (LOTAN) is given to capture the behavior characteristics of the acoustic wave in the thermoacoustic system. On this basis, the effects of acoustic boundary conditions and hysteresis time on the thermoacoustic instability of the combustion system are analyzed, and the relationship between the mode shape, pressure, vibration velocity phase, and thermoacoustic instability is explored. It is found that the phase relationship between pressure and vibration mode can be used to determine the thermoacoustic instability of the system. This is of great practical significance for determining the thermoacoustic instability of the system and clarifying the internal mechanism of its generation and provides theoretical support for the subsequent thermoacoustic instability control.

Inverse problem for wave equation of memory type with acoustic boundary conditions

In this article, for the direct problem, which consists of finding the velocity potential and the displacement of boundary points in the wave equation of memory type with initial and boundary acoustic conditions, the inverse problem of determining the memory kernel by the integral overdetermination condition is studied. By introducing a new function, the problem is reduced to a problem with homogeneous boundary conditions. Using the technique of estimating integral equations and the contraction mappings principle in Sobolev spaces, the existence and uniqueness theorem for the inverse problem is proved.

Results from a Nonlinear Wave Equation with Acoustic and Fractional Boundary Conditions Coupling by Logarithmic Source and Delay Terms: Global Existence and Asymptotic Behavior of Solutions

The nonlinear wave equation with acoustic and fractional boundary conditions, coupled with logarithmic source and delay terms, is significant for its ability to model complex systems, its contribution to the advancement of mathematical theory, and its wide-ranging applicability to real-world problems. This paper examines the global existence and general decay of solutions to a wave equation characterized by coupling with logarithmic source and delay terms, and governed by both fractional and acoustic boundary conditions. The global existence of solutions is analyzed under a range of hypotheses, and the general decay behavior is established through the construction and application of an appropriate Lyapunov function.

Ultralow-frequency absorption mechanism of a hybrid membrane resonator with acoustic soft boundary condition

Hybrid membrane resonator (HMR) as a typical metamaterial-based absorber with acoustic hard boundary condition (AHBC) has demonstrated excellent noise absorption abilities, but the challenge lies in achieving broadband absorption of ultralow-frequency noise in the tens of Hz to 150 Hz regime. In this research, we investigate systematically the absorption characteristics, absorption mechanisms, and casual optimality of an HMR with three openings in lower surface of the cavity, which functioned as an acoustic soft boundary condition (ASBC). Compared to the well-studied HMR with AHBC, a new absorption mechanism, which states that most energy dissipates occur in the opening region rather than in the membrane, has been found first. As a result, the HMR with ASBC can demonstrate outstanding ultralow-frequency sound absorption performance with a very small thickness, and the full width at half maximum of the HMR can be enlarged over 7 times. Furthermore, the causal inequalities of the absorbers with ideal AHBC and ASBC are derived based on the Cauchy integral and causality principle. The causal optimality of the proposed absorber is also achieved. This research provides valuable guidelines for the design of excellent ultralow-frequency sound absorbers which could contribute to solving the major issue of noise reduction.

An adjoint Green’s function approach for thermoacoustic instabilities in a duct with mean flow

Thermoacoustic instabilities arise from the feedback between an acoustic field and the unsteady heat released in a burner, yielding self-sustained oscillations. A fundamental framework for modelling thermoacoustic instabilities in systems where a mean flow is present is introduced, based on the definition of the adjoint Green’s function which permits to convert the acoustic analogy equation into an integral equation. The adjoint Green’s problem produces sensitivity functions which quantify the response of the system to initial, boundary or other forcing terms. A simple one-dimensional system is examined; it includes a steady uniform mean flow and a nonlinear heat source with an amplitude-dependent time-delay heat release model. The versatility of the approach is demonstrated by applying it to two resonators characterized by different acoustic boundary conditions: a Rijke tube and a quarter-wave resonator. The control parameters are: heat source position, heater power and tube length. The results reveal that the proposed analytical framework successfully captures the limit cycles, triggering phenomena, hystereses, and Hopf bifurcations observed in experiments. We show that the mean flow velocity cannot be discarded in the study of such systems; by increasing it, a stabilization generally ensues, with a modification of the bistability characteristics of the system.

Stability analysis for wave equations with variable exponents and acoustic boundary conditions

In this paper, we consider a wave equation with nonlinearities of variable exponents and acoustic boundary conditions. Using the multiplier method, we establish general stability results to the equation when the damping term has a time‐dependent coefficient and the exponent has extended range.

Stabilization and Blow-up in an Infinite Memory Wave Equation with Logarithmic Nonlinearity and Acoustic Boundary Conditions

Stabilization and Blow-up in an Infinite Memory Wave Equation with Logarithmic Nonlinearity and Acoustic Boundary Conditions

Analytical modeling of thermoacoustic instability influences in gas turbine combustors: A detailed parameter sensitivity analysis

In this study, the effects of various system parameters on combustion instability were numerically identified through a network-based thermoacoustic model using the concept of a transfer function. The acoustic transfer function was derived from the wave equation and various conservation laws in a two-duct system consisting of a nozzle and combustion chamber that is a simplified form of a gas turbine combustor. From the current numerical approach, the major parameters affecting the system acoustics, such as the duct length, area ratio, sound speed ratio, and Mach number, as well as the inlet and outlet acoustic boundary conditions, were defined explicitly, and a method for intuitively examining their influence was presented. The gain (nf) of the flame transfer function was noted to have a complex effect in combination with factors such as temperature ratio and area ratio, and the time delay (τf) was one main dominant factor that determined the main characteristics of instability, resulting in mode transition as well as changes in frequency and growth rate of the instability.

Three evolution problems modeling the interaction between acoustic waves and non-locally reacting surfaces

The paper deals with three evolution problems arising in the physical modeling of small amplitude acoustic phenomena occurring in a fluid, bounded by a surface of extended reaction. The first one is the widely studied wave equation with acoustic boundary conditions, but its derivation from the physical model is mathematically not fully satisfactory. The other two models studied in the paper, in the Lagrangian and Eulerian settings, are physically transparent. In the paper the first model is derived from the other two in a rigorous way, also for solutions merely belonging to the natural energy spaces.

Numerical study of the behavior of a near-wall bubble under the influence of an acoustic wave

Acoustic cavitation has been applied to many ultrasonic fields, but its characteristics are not fully understood, especially near the wall. To analyze the dynamics of a near-wall acoustic bubble, an acoustic pressure wave boundary condition is developed in the OpenFOAM platform. We first conducted the model’s validation with an experiment to prove its accuracy. The bubble’s radius increases when the bubble is excited by the lower-pressure wave, and it decreases under the higher-pressure wave. When the bubble collapses, its pressure and temperature will reach the maximum value. In accordance with the non-dimensional distance, the dynamics of the acoustic-driven bubble are classified into three types, i.e., the liquid jet not touching the nearby wall, the liquid jet touching the wall, and no obvious liquid jet. The maximum value of pressure and temperature increases with the dimensionless distance decreasing if the dimensionless distance is small. However, there is no variation of these peak values with dimensionless distance if the dimensionless distance is large.

Physics-informed neural networks for acoustic boundary admittance estimation

Acoustic simulations often face significant uncertainties due to limited knowledge of acoustic boundary conditions. While measuring the boundary admittance in situ is challenging in practical applications, numerical inverse methods can be used to characterize the boundary conditions based on sound pressure data. However, conventional inverse methods require a validated forward model and can become impractical for computationally expensive simulation models. Over the past years, machine learning approaches have emerged as promising methods for scientific computing and data-driven modeling. Physics-informed neural networks incorporate physical prior knowledge into a neural network by adding the residual of the underlying partial differential equation to the loss function. Training the neural network minimizes the loss function, allowing the network to learn a solution that not only fits the training data but also satisfies the corresponding boundary value problem. In this study, physics-informed neural networks are trained to learn the sound pressure solution within two numerical examples governed by the Helmholtz equation without explicitly specifying the boundary conditions at selected boundaries. After training, the neural network’s prediction of the boundary admittance is evaluated and compared to the ground truth, initially assigned in the finite element reference solution. Additionally, the proposed method is validated using experimental data obtained from an acoustic impedance tube measurement. The results show that physics-informed neural networks can accurately learn the sound pressure field and implicitly solve the inverse problem by providing an accurate estimate of the underlying boundary admittance, even in the case of spatially varying boundary conditions.

General energy decay estimates for a variable coefficient viscoelastic semilinear wave equation with logarithmic source term and acoustic boundary conditions

In this paper, we consider a variable coefficient viscoelastic semilinear wave equation with logarithmic source term and acoustic boundary conditions in domains with non‐locally reacting boundary. By potential well method, we get the global existence of solution and through several important lemmas, we prove the general energy decay estimate of the system.

On the application of acoustic liners for the reduction of jet-flap installation noise

In this work, an experimental and numerical analysis of the feasibility of using acoustic liners to reduce the acoustic far-field radiation of a subsonic jet near a flat plate is presented. The Boundary Element Method (BEM) with a wavepacket model of the jet noise and considering an acoustic impedance boundary condition was used to calculate the far-field noise for different conditions. A parametric optimization was performed in order to find an optimum impedance in terms of the Overall Sound Pressure Level reduction. Semi-empirical models of acoustic liners were then used to design a liner with an impedance as close as possible to the optimum impedance. The liners were built using additive manufacturing and tested in terms of their acoustic impedance and the resulting noise reduction when applied to a region of the flat plate. The BEM simulations, considering the impedance, showed good agreement with experimental data. Overall, by means of the BEM model, optimization and liner semi-empirical models, it was possible to design an acoustic liner which significantly reduced the installation noise at the far-field, with the overall noise reduction between 2 dB to 4 dB depending on observation angle.

Dynamic stiffness formulations for exact modal and dynamic response analysis of three-dimensional acoustic cavities in cylindrical coordinates

Exact dynamic stiffness (DS) models for three-dimensional (3D) cavities in cylindrical coordinates under any classical acoustic boundary conditions (BCs) are proposed in this paper. The paper first derives the exact general solutions that satisfy the governing differential equations. Then, these general solutions are used to develop the DS matrices for 3D cavities in cylindrical coordinates by substituting them into the acoustic pressure and normal velocity BCs. Subsequently, the Wittrick–Williams algorithm, along with the analytical expressions of the j0 count for various shaped cavities, is applied to compute natural frequencies. Finally, reliable and efficient techniques for dynamic response solution are employed. The DSM provides benchmark solutions for various 3D cavities. The convergence, universality, and efficiency of the proposed method in modal and response analysis are illustrated by comparing the results obtained using the DSM and FEM. The calculation time when using the DSM is only 0.1% of that when using the commercial finite element method, while maintaining the same accuracy. This research not only provides an effective technique for analyzing the cylindrical acoustic pressure field in engineering, but also establishes a foundation for the analysis of structural–acoustic coupling in tubular structures.

On a coupled system of viscoelastic wave equation of infinite memory with acoustic boundary conditions

This work deals with a coupled system of viscoelastic wave equation of infinite memory with mixed Dirichlet-Neumann boundary conditions. The coupling is via the acoustic boundary conditions on a portion of the boundary. The semigroup theory is used to show the well-posedness and regularity of the initial and boundary value problem. Moreover, we investigate exponential stability of the system taking into account Gearhart-Prüss’s theorem. Mathematics Subject Classification (2010): 35A01, 74B05, 93D15. Received 11 June 2021; Accepted 13 October 2021

Measuring the internal damping of thin metal beams in flexure

Since the internal damping of most metals is a relatively small quantity, precise measurement requires that both acoustic radiation damping and boundary condition damping be either eliminated or highly minimized. In this talk, an experiment setup will be described which can measure the internal damping of metal beams in flexure. To perform a measurement, a beam specimen is placed on wire supports within a vacuum chamber and excited by an autonomous force hammer located within the chamber. The wire supports are located exactly at the nodal lines of the beam mode of interest, so that the frictional losses created by the wire supports are minimized. Once excited, the beam deflection is measured with a single point laser vibrometer. The signal decay measured by the vibrometer is used to estimate damping of the mode of interest using either the Hilbert transform or the half- power method. The wire supports are then moved, and the procedure is repeated for the next mode of interest. Results for several metal specimens will be presented and compared to Zener’s thermoelastic model, which describes the losses created by thermal currents for a beam in flexure, to demonstrate the accuracy of the measurement method.

General decay of a variable coefficient viscoelastic wave equation with the logarithmic nonlinearity, not necessarily decreasing kernel and acoustic boundary conditions

General decay of a variable coefficient viscoelastic wave equation with the logarithmic nonlinearity, not necessarily decreasing kernel and acoustic boundary conditions