Acoustics of a blocked duct with flow

An analysis is given for flow and acoustical motion of fluid in a duct, aimed at describing some features of the blowing mechanism of a woodwind instrument. The latter is simulated by a rigid rectangular duct, open at one end and nearly closed off at the other, where a local section of the side wall can undergo transverse displacement. It is supposed that such a piston-like oscillation superposes an acoustical perturbation on a steady flow through the duct. The principal results of the calculations, in which it is presupposed that the displacement amplitude is small compared to the piston width, which is in turn small compared with the duct width and wavelength, are contained in estimates for the natural frequencies and optimum flow speeds to excite these modes.     

Reflection of sound at area expansions in a flow duct

An analytical model for scattering at area discontinuities and sharp edges in flow ducts and pipes is presented. The application we have in mind is large industrial duct systems, where sound attenuation by reactive and absorptive baffle silencers is of great importance. Such devices commonly have a rectangular cross-section, so the model is chosen as two-dimensional. Earlier solutions to this problem are reviewed in the paper. The modelling of the flow conditions downstream of the area expansion, with and without extended edges, and its implications for the resulting acoustic modes are discussed. Here, the scattering problem is solved with the Wiener-Hopf technique, and a Kutta condition is applied at the edge. The solution of the wave equation downstream of the expansion includes hydrodynamic waves, of which one is a growing wave. Theoretical results are compared with experimental data for the reflection coefficient for the plane wave, at frequencies below the cut-on for higher order modes. Influence of the interaction between the sound field and the flow field is discussed. A region where the reflection coefficient is strongly Strouhal number dependent is found.     

Prediction of flow-generated noise produced by acoustic and aerodynamic interactions of multiple in-duct elements

Flow-generated noise problem caused by in-duct elements is due to the complicated acoustic and turbulent interactions of multiple in-duct flow noise sources. The approach of partially coherent sound fields used previously by Mak and Yang [C.M. Mak, J. Yang, Flow-generated noise radiated by the interaction of two strip spoilers in a low speed flow ducts, Acta Acust united with Acustica 88 (2002) 861–868] and Mak [C.M. Mak, A prediction method for aerodynamic sound produced by multiple elements in air ducts, J Sound Vib 287 (2005) 395–403] is adopted to formulate the sound powers produced by interactions of multiple elements at frequencies below and above the cut-on frequency of the lowest transverse duct mode. The study indicates that the level and spectral distribution of the additional acoustic energy produced by the interactions of multiple elements can be predicted based on the measured data with respect to the interactions. The proposed method can form a basis of a generalized prediction method for flow-generated noise produced by multiple elements. The application of the proposed method is supported by two engineering examples.     

The acoustic characteristics of duct bends

The acoustic characteristics of a duct system were studied. The system consisted of a curved bend joined to two straight sections of rigid duct. Solutions of the relevant two-dimensional equations were obtained by numerical methods for a range of bend geometries. The results agreed closely with experimentally obtained data. The effects on the acoustic characteristics of locating a circular arc turning vane in the bend were investigated numerically and experimentally for values of the wave number below that corresponding to the first cut-on mode. Particular attention was paid to the amplitude of the evanescent modes generated at the junction of the bend and the straight sections of duct.     

Broadband noise prediction of fan outlet guide vane using a cascade response function

An analytical model of the broadband noise produced by both the interaction of ingested turbulence with a fan rotor blades and the rotor-wake impingement on downstream stator vanes is proposed and detailed. The noise prediction methodology is a strip-theory approach based on a previously published formulation of the three-dimensional unsteady blade loading for a rectilinear cascade. This three-dimensional cascade response applied in each strip combined with an acoustic analogy in an annular duct have been chosen to account for the main three-dimensional effects. To further improve some of the identified limitations of this approach, a correction is added to mitigate the effects of the non-coincidence of the cut-on frequencies of the annular duct modes and of the modes of the rectilinear cascade. A correction of the unsteady blade loading formulation, previously developed in a tonal configuration, is also introduced to account for the dispersion relation of annular duct modes in the rectilinear-cascade model. The model is compared with experimental results of the 22-in source diagnostic test (SDT) fan rig of the NASA Glenn Research Center. A numerical assessment of the simplifications proposed in the model and of the convergence of the truncated sums in spanwise wavenumbers and azimuthal orders of the incident perturbation is carried out. The subcritical gusts are shown to have a crucial effect at low frequencies, whereas they become negligible at higher frequencies. Furthermore, alternative high-frequency formulations lead to a satisfactory accuracy above a Helmholtz number based on the duct radius of 20. The strong reduction in computational time associated with these formulations could justify their use for parametric studies in industrial context. The effect of the turbulence model is also investigated showing the relevance of Liepmann's isotropic model in the SDT case, and a possible strong effect of anisotropy in static tests. Finally, the model is compared with NASA's experimental results for two outlet guide vanes at approach condition, showing a very good agreement upstream, whereas an underestimate of 3-5 dB is observed downstream in the middle frequency range.     

Collective excitations in exciton crystal

Crystal phase of indirect excitons formed by spatially separated electrons and holes in coupled quantum wells is analyzed. The collective mode spectrum of the exciton crystal at zero and nonzero agnetic fields is found. The spectrum consists of two optical and two acoustical modes (transverse and longitudinal in each case). We also study changes of the dipole crystal collective excitations at the transition exciton crystal-electron-hole plasma.     

A finite element model for rigid porous absorbing materials

An eight node isoparametric finite element is used to represent a rigid porous absorbing material. Tests on an assembly of these elements for a one dimensional model gave good agreement with an exact solution for the input impedance. Results from a two dimensional model show the effects of transverse propagating modes on the input impedance and indicate that for an absorbent with finite dimensions extended reaction is important.     

Mode detection in turbofan inlets from near field sensor arrays

Knowledge of the modal content of the sound field radiated from a turbofan inlet is important for source characterization and for helping to determine noise generation mechanisms in the engine. An inverse technique for determining the mode amplitudes at the duct outlet is proposed using pressure measurements made in the near field. The radiated sound pressure from a duct is modeled by directivity patterns of cut-on modes in the near field using a model based on the Kirchhoff approximation for flanged ducts with no flow. The resulting system of equations is ill posed and it is shown that the presence of modes with eigenvalues close to a cutoff frequency results in a poorly conditioned directivity matrix. An analysis of the conditioning of this directivity matrix is carried out to assess the inversion robustness and accuracy. A physical interpretation of the singular value decomposition is given and allows us to understand the issues of ill conditioning as well as the detection performance of the radiated sound field by a given sensor array.     

Self-induced sound generation by flow over perforated duct liners

An adverse “singing” phenomenon due to flow over perforated liners in a duct was studied experimentally. The liners consisted of honeycomb structures bonded to and sandwiched between two flat aluminum skins. The inner skin in contact with the flow had holes (perforations) with pitch distances either equal to or different from those of the honeycomb structures, forming, respectively, narrow-band or broadband liners. The shedding of vortices in the flow over these holes induced excitation of acoustic modes within the duct, and under the condition whereby the cut-on frequency of an excited mode coincided with, or was very near to, the shedding frequency a very strong tone corresponding to that particular modal cut-on frequency resulted. For narrow-band liners, the “singing” phenomenon could also be induced by cavity resonance. The shedding frequency increased with increase in flow velocities and thus higher order acoustic modes were excited consecutively in a similar manner. The Strouhal number calculated from the observed shedding frequency and the flow velocity was found to vary directly with the hole diameter of the perforate. The high signal to noise ratio during the peak of self-excitation presents a new method in the determination of the wall admittance under the flow conditions.     

Dynamics of bi-periodic structures

Many structures considered for space applications are bi-periodic in their construction. Bi-periodicity means that two types of structural subassemblies, alternating in one or more directions, make up the structure. To gain insight into the dynamics of bi-periodic space structures a variety of one and two dimensional bi-periodic structures are considered. Results indicate that bands in which natural frequencies lie for periodic structures are further subdivided as a consequence of the bi-periodicity. Analytical solutions for the modes and frequencies of finite length one dimensional bi-periodic structures are obtained for general boundary conditions. A transmission method is developed to simplify the application of boundary conditions. It is found that some modes occur at frequencies which are outside the frequency bands predicted for bi-periodic structures. Two dimensional bi-periodic crossed beam grillage and truss structures are considered in this study. For cases where a separation of variables solution is possible the two dimensional structures exhibit similar properties to the one dimensional bi-periodic structures. Analytical solutions for the one and two dimensional bi-periodic structures considered above lead to a compact solution form similar to that of periodic structures analysis.     

Parametric study of a drum-like silencer

An optimization study is carried out for a silencer consisting of two side-branch, rectangular cavities covered by membranes highly stretched in the direction of the duct axis. Stopband is defined as the range of frequency where the transmission loss is everywhere higher than the peak value of that in an expansion chamber which occupies three times as much cavity volume as does the present silencer. The logarithmic bandwidth is optimized with respect to the length-to-depth ratio of the cavity, the mass and the tension of the membrane. For two cavities each with a dimensionless volume of 5 (the duct height being the length scale), the optimal cavity aspect ratio is 6.6, and the lower stopband frequency is 0.09 times the first cut-on frequency of the rigid duct. This is compared favourably with the traditional duct lining modelled as an equivalent fluid. As the membrane mass increases, the stopband shifts to lower frequencies but it also narrows. The widest stopband is around 1.6 octaves for a massless membrane. The membrane tension plays a delicate role of setting the intervals between adjacent spectral peaks.     

Effects of surface relaxation on the surface modes of a CsCl (001) slab shaped crystal

The vibrational frequencies of a 24-layer CsCl (001) slab have been calculated with an eleven-parameter shell model. Without surface relaxation, the results exhibit an instability in the form of a pair of imaginary-frequency Rayleigh modes for wave vectors over most of the surface Brillouin zone. To investigate the effects of relaxation on this dynamic instability, two kinds of relaxation have been used; (i) an inward relaxation of the two outermost planes, and (ii) an expansion of the entire slab in the z-direction (i.e. normal to the surfaces), followed by an inward relaxation of the two outermost planes. In the first case, the imaginary frequencies are removed for most wave vectors except for those very close to the zone center. In the second case, the imaginary frequencies are removed for all wave vectors. Due to the occurrence of two different surfaces of the slab, one containing only Cs⁺ ions, the other only Cl^? ions, two classes of surface modes are found: one with the vibrational amplitudes decreasing from the top layer to the bottom layer, the other vice versa. Longitudinal and transverse optical, and transverse accoustical surface modes are found in both classes. The frequencies of these surface modes are strongly dependent on the surface relaxations.     

矩形辐射器压电多频超声换能器的研究

研究了一种具有多个共振频率的矩形辐射器夹心式超声换能器,换能器由圆柱形后盖板、压电陶瓷晶堆及矩形六面体辐射器前盖板组合而成。利用表观弹性法和一维近似理论给出了多频换能器横向及纵向理论共振频率方程。对一种特殊情况下的此类换能器进行了有限元及实验分析,给出了各自的频率输入导纳曲线。对理论和实验结果进行分析后表明,此类矩形辐射器夹心式超声换能器可以在不同的振动模态上工作,具有多个共振频率.     

Observation of the transverse optical plasmon in SmLa0.8Sr0.2CuO4-delta

We present microwave and infrared measurements on SmLa0.8Sr0.2CuO4-delta, which are direct evidence for the existence of a transverse optical plasma mode, observed as a peak in the c-axis optical conductivity. This mode appears as a consequence of the existence of two different intrinsic Josephson couplings between the CuO2 layers, one with a Sm2O2 block layer, and the other one with a (La,Sr)2O2-delta block layer. From the frequencies and the intensities of the collective modes we determine the value of the compressibility of the two dimensional electron fluid in the copper oxygen planes.     

Tracking spatial modes in nearly hemispherical microcavities

We measure experimentally the spatial intensity profiles and resonant frequencies of the transverse modes of nearly hemispherical microcavities with cavity length and mirror curvatures below 10 microm. These resonators possess axially symmetric Gauss-Laguerre-like modes, but do not display the frequency degeneracies typical of large-scale optical cavities. It is possible to interpret these results using a paraxial model of cavity propagation that includes nonparabolic optical elements.     

Investigation into higher-order mode propagation through orifice plates in circular ducts

Most established techniques for analyzing sound transmission in ducts containing orifices plates are only applicable for plane wave propagation. Once the wavelength of the sound approaches the cross section of the duct, higher order mode propagation in the system must be considered in the analysis. This is a numerically intensive activity if fully coupled calculations of the higher order modes are undertaken. This investigation estimates the acoustic fields in a duct with a simple orifice plate installed using an uncoupled model to estimate the higher order mode contribution. The uncoupled model is then used as the basis for a hybrid decomposition approach to estimate the sound field in the regions before and after the orifice plate installed in a circular duct. This approach is applied to a duct, excited by a point source over a wide frequency range, containing a single orifice plate installed a distance inside the duct. Different orifice plates with one, two and multiple openings are investigated. Of particular interest is the location of the point source relative to the duct axis. If the source is located concentric to the duct axis then, without any orifice plate present, only axially symmetric higher order modes may be excited in the duct. Thus, the investigation considers the point source located in the concentric position and in eccentric positions to vary the contribution from the different types of higher order mode. Estimates of the acoustic fields in the duct obtained using the hybrid decomposition approach are compared with measured data and the applicability of using an uncoupled estimate for the acoustic fields is commented on.     

Sensitivity of a continuum vocal fold model to geometric parameters, constraints, and boundary conditions

The influence of key dimensional parameters, motion constraints, and boundary conditions on the modal properties of an idealized, continuum model of the vocal folds was investigated. The Ritz method and the finite element method were used for the analysis. The model's vibratory modes were determined to be most sensitive to changes in the anterior-posterior length of the vocal fold model, due to the influence of three-dimensional stress components acting in the transverse plane. Anterior/ posterior boundary conditions were found to have a significant influence on the vibratory response. Overestimation of modal frequencies resulted when vibration of the structure was restricted to the transverse plane. The overestimation of each modal frequency was proportional to the ratio of longitudinal to transverse Young's modulus, and was significant for ratio values less than 20.     

Finite element formulations for acoustical radiation

Finite and infinite element techniques are applied to linear acoustical problems involving infinite anechoic boundaries. Theory is presented for a simple one dimensional model based on Webster's horn equation. Results are then presented both for the one dimensional model and for two axisymmetric test cases. Comparisons with exact solutions indicate that both the infinite element and wave envelope schemes are effective in correctly predicting the near field. The wave envelope scheme is also shown to be capable of resolving the far field radiation pattern.     

Free vibrations of an infinite plate of parabolically varying thickness on elastic foundation

A simple model is presented for use by research workers in seismology, soil mechanics and earthquake vibrations in problems where the resistance offered by the soil foundation is very close to that of Winkler's assumption. In earth vibrations one earth layer can be treated as an infinite plate of variable thickness while layers below it may approximately serve as an elastic foundation. Here, the transverse displacement of a plate of parabolically varying thickness on an elastic foundation is expressed as a power series and the frequencies, deflections and moments corresponding to the first two modes of vibration are computed for various values of foundation modulus and taper constant, and for two combinations of boundary conditions. A problem discussed in previous work [1] can be considered as a particular case of the present problem if the foundation modulus is taken to be zero.