Acoustic Boundary Conditions Research Articles

Joint parameter identification, vibration and noise analysis of gearbox

A certain type of gearbox is investigated for the problem that the stiffness and damping of bearings are difficult to be accurately determined and then affect the analysis of vibration and noise of gearbox. Firstly, a coupled dynamic lumped parameter model of three-stage helical gear system with consideration of bearing stiffness, bearing damping, and transmission error is established. The modal parameters of gear system are obtained by using the experimental modal analysis method with single-input and multiple-output. The equation for joint parameter identification of gearbox is established which is based on the experimental modal analysis theory and the dynamic lumped parameter model, and subsequently the parameters of the joint are obtained by the least square method. Then, a gear-shaft-bearing- housing coupled dynamic finite element model is developed on the basis of the identified parameters, and after that the dynamic response results of gearbox are solved by using the modal superposition method and compared with the vibration test results. Finally, an acoustic boundary element model of gearbox is established by taking the dynamic response results as the acoustic boundary condition, and the surface sound pressure and radiation noise of gearbox are solved by the boundary element method (BEM), and then the results are compared with the noise test. The results show that the simulation laws and test laws are in good agreement, and thus the method of joint parameter identification, vibration and noise analysis of gearbox is feasible.

Energy decay of variable‐coefficient wave equation with nonlinear acoustic boundary conditions and source term

In this paper, we consider a variable‐coefficient wave equation with nonlinear acoustic boundary conditions and source term. Using the Riemannian geometry method, we prove the general energy decay of the system corresponds to the ordinary differential equation (ODE), which certainly is stable under some suitable assumptions.

Grasp of the influence of temperature distribution in the tube simulating a gas turbine combustor on acoustic boundary conditions

Grasp of the influence of temperature distribution in the tube simulating a gas turbine combustor on acoustic boundary conditions

DYNAMIC PROPERTIES FOR NONLINEAR VISCOELASTIC KIRCHHOFF-TYPE EQUATION WITH ACOUSTIC CONTROL BOUNDARY CONDITIONS Ⅱ

In this paper, we consider the nonlinear viscoelastic Kirchhoff-type equation with initial conditions and acoustic boundary conditions. Under suitable conditions on the initial data, the relaxation function h(·) and M(·), we prove that the solution blows up in finite time and give the upper bound of the blow-up time T*.

Analysis of Acoustic Characteristics of Arbitrary Triangular Prism and Quadrangular Prism Acoustic Cavities

This paper proposes a method for the analysis of acoustic modals and steady‐state responses of arbitrary triangular prism and quadrangular prism acoustic cavities based on the three‐dimensional improved Fourier series. First, the geometric models of arbitrary triangular prism and quadrangular prism acoustic cavities are established. To facilitate the calculation, the bottom and top surfaces of the irregular cavity are converted into the unit square domain by a coordinate transformation. Internal sound pressure‐admissible functions are constructed, and energy expressions are derived after coordinate transformation based on the three‐dimensional improved Fourier series. The acoustic modals of arbitrary triangular prism and quadrangular prism acoustic cavities are obtained by the Rayleigh–Ritz technique. At the same time, a point sound source excitation is introduced into the cavity to further study the steady‐state responses of prismatic acoustic cavities with different acoustic impedance boundary conditions. The reliability and universality of the method are verified by comparing with the finite element results. The method and results can provide some references and benchmarks for future research and application.

Dynamic Properties of a Nonlinear Viscoelastic Kirchhoff-Type Equation with Acoustic Control Boundary Conditions. I

В данной работе рассматривается нелинейное уравнение вязкоупругости типа Кирхгофа $$ u_{tt}-M(\|\nabla u\|^2_2)\Delta u +\int_0^t h(t-s)\Delta u(s) ds+a|u_t|^{m-2}u_t=|u|^{p-2}u $$ с начальными условиями и акустическими граничными условиями. В зависимости от свойств ядер свертки $h$ на бесконечности будет показано, что энергия решения убывает экспоненциально или полиномиально при $t\to +\infty$. Наш подход основан на использовании техники интегральных неравенств и множителей. Вместо того чтобы применять технику типа Ляпунова к некоторой возмущенной энергии, мы рассмотрим исходную энергию и покажем, что она удовлетворяет нелинейному интегральному неравенству, которое, в свою очередь, дает окончательную оценку убывания. Библиография: 33 названия.

부분 예혼합 화염의 연료 조성에 따른 연소불안정 특성

Combustion instability of synthetic gas in a partially-premixed combustor has been numerically investigated by varying H₂ percentage of the fuel composition. During predictions with utilization of a lumped network code, the effects of different flame transfer function (FTF) models, which include the 2SUPnd/SUP order filter model and the state space model, and acoustic boundary conditions have also been investigated. The predicted results quite agree well with the corresponding experimental ones.

Effects of Central Tube on Shape of Modal Duct of a Helicoid in a Simple Expansion Chamber

The shape of the modal duct of an acoustic wave propagating in a muffling system varies with the internal geometry. This shape can be either as a result of plane wave propagation or three-dimensional wave propagation. These shapes depict the distribution of acoustic pressure that may be used in the design or modification of mufflers to create resonance at cut-off frequencies and hence achieve noise attenuation or special effects on the output of the noise. This research compares the shapes of acoustic duct modes of two sets of four pitch configurations of a helicoid in a simple expansion chamber with and without a central tube. Models are generated using Autodesk Inventor modeling software and imported into ANSYS 18.2, where a fluid volume from the complex computer-aided-design (CAD) geometry is extracted for three-dimensional (3D) analysis. Mesh is generated to capture the details of the fluid cavity for frequency range between 0 and 2000Hz. After defining acoustic properties, acoustic boundary conditions and loads were defined at inlet and outlet ports before computation. Postprocessed acoustic results of the modal shapes and transmission loss (TL) characteristics of the two configurations were obtained and compared for geometries of the same helical pitch. It was established that whereas plane wave propagation in a simple expansion chamber (SEC) resulted in a clearly defined acoustic pressure pattern across the propagation path, the distribution in the configurations with and without the central tube depicted three-dimensional acoustic wave propagation characteristics, with patterns scattering or consolidating to regions of either very low or very high acoustic pressure differentials. A difference of about 80 decibels between the highest and lowest acoustic pressure levels was observed for the modal duct of the geometry with four turns and with a central tube. On the other hand, the shape of the TL curve shifts from a sinusoidal-shaped profile with well-defined peaks and valleys in definite multiples of π for the simple expansion chamber, while that of the other two configurations depended on the variation in wavelength that affects the location of occurrence of cut-on or cut-off frequency. The geometry with four turns and a central tube had a maximum value of TL of about 90 decibels at approximately 1900Hz.

Blow‐up of solution of wave equation with internal and boundary source term and non‐porous viscoelastic acoustic boundary conditions

AbstractIn this paper we study the blow‐up of solution of a mixed problem associated to a nonlinear wave equation with dissipative and source term in a bounded domain of . On a boundary portion of the domain we consider a non‐porous viscoelastic acoustic boundary conditions to a non‐locally reacting boundary.

A global nonexistence of solutions for a quasilinear viscoelastic wave equation with acoustic boundary conditions

In this paper, we consider a quasilinear viscoelastic wave equation with acoustic boundary conditions. Under some appropriate assumption on the relaxation function g, the function Φ, p > max { rho +2, m, q,2}, and the initial data, we prove a global nonexistence of solutions for a quasilinear viscoelastic wave equation with positive initial energy.

Scattering of low frequency sound by fluid and solid cylinders

Wave scattering by objects is typically studied for plane incident waves. However, full Green's functions are necessary for problems where the separation of the scatterer from interfaces, sources, or other scatterers is comparable to the dimensions of the scatterer itself. In this paper, the two-dimensional problem of scattering of monochromatic cylindrical waves by an infinite cylinder embedded in a homogeneous fluid is considered. Fluid and solid cylinders are studied, and soft and hard cylinders are revisited. The exact solutions for the Green's functions are expressed as an infinite series of cylindrical functions with complex amplitudes determined by the acoustic boundary conditions at the surface of the cylinder. Here, we derive closed-form asymptotics for the scattered field in the Rayleigh scattering regime where radius of the cylinder is small compared to the wavelength. The scattered wave approximation is valid for arbitrary source and observation point positions outside the scatterer and is expressed as a sum of fields due to three linear image sources. When the source or receiver is located sufficiently far from the cylinder, the new uniform asymptotic solutions reduce to well-known results for plane-wave scattering. Image source solutions were anticipated due to classically studied electrostatic analog problems involving dielectric cylinders. Image source representation offers physical insights into the scattering physics and suggests simple analytic solutions for scattering by objects near interfaces and within waveguides.

Non-dimensional groups for similarity analysis of thermoacoustic instabilities

An approach for similarity analysis of thermoacoustic combustion instabilities is proposed. A set of non-dimensional Π-groups is deduced from a solution based on modal expansion of the quasi-1D Helmholtz equation with a time-lagged heat source. Although thermoacoustic stability depends on a considerable number of parameters, which describe the geometry and thermodynamic characteristics of a combustor, the acoustic boundary conditions, the strength of flow-flame-acoustic coupling, etc., it is found that the respective non-dimensional frequencies and growth rates of thermoacoustic modes are dominated by only two Π-groups: Firstly, flame potency, which is governed by the intensity of mean and fluctuating rate of heat release and a parameter that quantifies the strength of flame-acoustic interaction for a given mode. The second Π-group is the non-dimensional time lag of the flame. Eigenfrequency locus plots for three combustor configurations are generated by varying interaction index and time lag of the flame model. It is found that similarity analysis explicates universal features of thermoacoustic instability and helps to classify thermoacoustic modes. Moreover, similarity analysis establishes not only the stability of eigenmodes, but also the sensitivity of eigenfrequency or growth rate to changes of any parameter contained in any of the two Π groups. In closing, the relevance of flame potency for the design of stable combustors is discussed.

Unified error analysis for nonconforming space discretizations of wave-type equations

AbstractThis paper provides a unified error analysis for nonconforming space discretizations of linear wave equations in the time domain. We propose a framework that studies wave equations as first-order evolution equations in Hilbert spaces and their space discretizations as differential equations in finite-dimensional Hilbert spaces. A lift operator maps the semidiscrete solution from the approximation space to the continuous space. Our main results are a priori error bounds in terms of interpolation, data and conformity errors of the method. Such error bounds are the key to the systematic derivation of convergence rates for a large class of problems. To show that this approach significantly eases the proof of new convergence rates, we apply it to an isoparametric finite element discretization of the wave equation with acoustic boundary conditions in a smooth domain. Moreover, our results reproduce known convergence rates for already investigated conforming and nonconforming space discretizations in a concise and unified way. The examples discussed in this paper comprise discontinuous Galerkin discretizations of Maxwell’s equations and finite elements with mass lumping for the acoustic wave equation.

Asymptotic behavior for a past history viscoelastic problem with acoustic boundary conditions

ABSTRACTIn this paper, we consider a viscoelastic equation of variable coefficients in the presence of infinite memory (past history) with nonlinear damping term and nonlinear delay term in the boundary feedback and acoustic boundary conditions. Under suitable assumptions, two arbitrary decay results of the energy solution are established via suitable Lyapunov functionals and some properties of the convex functions. The first stability result is given with a relation between the damping term and relaxation function and the second result is given without imposing any restrictive growth assumption on the damping term and the kernel function g. Our result extends the decay result obtained for problems with finite history to those with infinite history.

발전용 모델 가스터빈 연소기의 입구에서 음향반사계수 결정

A phenomenon that potentially influences the reliability of power generation systems is the presence of thermo-acoustic oscillations in the combustion chamber of a land- based gas turbine. To develop specific measures that prevent the instability, it is essential to predict and/or evaluate the underlying physics of the thermo-acoustics, which requires the acoustic boundary condition at the exit of the burner, that is, at the inlet of the combustor. Here we report a procedure for calculating acoustic reflection coefficients at the burner exit by utilizing two microphone method (TMM) for dynamic pressure signals. The procedure has been verified by comparing its results with reported ones and further successfully employed to determine the acoustic boundary condition of the burner of a partially-premixed model gas turbine combustor.

Optimizing piezoelectric receivers for acoustic power transfer applications

In this paper, we aim to optimize piezoelectric plate receivers for acoustic power transfer applications by analyzing the influence of the losses and of the acoustic boundary conditions. We derive the analytic expressions of the efficiency of the receiver with the optimal electric loads attached, and analyze the maximum efficiency value and its frequency with different loss and acoustic boundary conditions. To validate the analytical expressions that we have derived, we perform experiments in water with composite transducers of different filling fractions, and see that a lower acoustic impedance mismatch can compensate the influence of large dielectric and acoustic losses to achieve a good performance. Finally, we briefly compare the advantages and drawbacks of composite transducers and pure PZT (lead zirconate titanate) plates as acoustic power receivers, and conclude that 1–3 composites can achieve similar efficiency values in low power applications due to their adjustable acoustic impedance.

Uniform stabilization of wave equation with localized internal damping and acoustic boundary condition with viscoelastic damping

In this paper, we deal with the uniform stabilization to the mixed problem for a nonlinear wave equation and acoustic boundary conditions on a non-locally reacting boundary. The main purpose is to study the stability when the internal damping acts only over a subset $$\omega $$ of the domain $$\Omega $$ and the boundary damping is of the viscoelastic type.

Global nonexistence of solutions for a nonlinear wave equation with time delay and acoustic boundary conditions

We consider a quasilinear wave equation utt−△ut−div(|∇u|α−2∇u)−div(|∇ut|β−2∇ut)+a|ut|m−2ut+μ1ut(x,t)+μ2ut(x,t−τ)=b|u|p−2ua,b>0, associated with initial and Dirichlet boundary conditions at one part and acoustic boundary conditions at another part, respectively. We prove, under suitable conditions on α, β, m, p and for negative initial energy, a global nonexistence of solutions.

Acoustic wave motions stabilized by boundary memory damping II. Polynomial stability

A linear wave equation with acoustic boundary conditions (ABC) on a portion of the boundary and Dirichlet conditions on the rest of the boundary is considered. The ABC contain a memory damping with respect to the normal displacement of the boundary point. In this paper, we establish polynomial energy decay rates for the wave equation by using resolvent estimates.

Self-sustained, high-frequency detonation wave generation in a semi-bounded channel

Combustion dynamics in a linear, semi-bounded channel were studied to characterize injection, mixing, and ignition processes in a two dimensional analogue of a rotating detonation wave combustor. The linear channel was developed to operate using natural gas and oxygen and to provide large optical accessibility in support of high-fidelity diagnostics at thermal power density levels representative of rotating detonation wave combustors over a broad range of flow conditions. Measurements of pressure and heat release were performed using an array of high-frequency dynamic pressure probes and OH*-chemiluminescence, respectively. Self-sustained, periodic generation of detonation waves was observed. These traveling combustion waves were initiated from low amplitude deflagrative fronts and steepened as they traveled through the combustion channel. The sensitivity of this instability to changes in acoustic boundary conditions was explored to determine the origin of the high-amplitude dynamics. The change in acoustic boundary at the end-wall affected the transverse acoustic mode frequency as expected, but had no effect on the detonation wave initiation. The detonation wave dynamics were found to be correlated with resonant frequencies in the propellant manifolds. It was determined that the frequency of the self-sustained chamber dynamics depends on which manifold has the strongest injection pressure ratio. OH*-chemiluminescence and pressure measurements indicate that the observed transition to detonation is linked to the auto-ignition of the reactants and that the auto-ignition event is coupled with the fluctuation in reactant mass flow associated with the manifold dynamics.