Trapped modes and Fano resonances in two-dimensional acoustical duct–cavity systems

2012 ◽  
Vol 692 ◽  
pp. 257-287 ◽  
Author(s):  
Stefan Hein ◽  
Werner Koch ◽  
Lothar Nannen
Keyword(s):  
Low Frequency ◽  
Sound Transmission ◽  
Side Branch ◽  
Absorbing Boundary Conditions ◽  
Infinite Length ◽  
Two Dimensional ◽  
Trapped Modes ◽  
Complex Scaling Method ◽  
Trapped Mode ◽  
Transmission And Reflection

AbstractRevisiting the classical acoustics problem of rectangular side-branch cavities in a two-dimensional duct of infinite length, we use the finite-element method to numerically compute the acoustic resonances as well as the sound transmission and reflection for an incoming fundamental duct mode. To satisfy the requirement of outgoing waves in the far field, we use two different forms of absorbing boundary conditions, namely the complex scaling method and the Hardy space method. In general, the resonances are damped due to radiation losses, but there also exist various types of localized trapped modes with nominally zero radiation loss. The most common type of trapped mode is antisymmetric about the duct axis and becomes quasi-trapped with very low damping if the symmetry about the duct axis is broken. In this case a Fano resonance results, with resonance and antiresonance features and drastic changes in the sound transmission and reflection coefficients. Two other types of trapped modes, termed embedded trapped modes, result from the interaction of neighbouring modes or Fabry–Pérot interference in multi-cavity systems. These embedded trapped modes occur only for very particular geometry parameters and frequencies and become highly localized quasi-trapped modes as soon as the geometry is perturbed. We show that all three types of trapped modes are possible in duct–cavity systems and that embedded trapped modes continue to exist when a cavity is moved off centre. If several cavities interact, the single-cavity trapped mode splits into several trapped supermodes, which might be useful for the design of low-frequency acoustic filters.

scholarly journals Trapped modes in a waveguide with a long obstacle

2000 ◽  
Vol 403 ◽  
pp. 251-261 ◽  
Author(s):  
N. S. A. KHALLAF ◽  
L. PARNOVSKI ◽  
D. VASSILIEV
Keyword(s):  
Two Dimensional ◽  
Trapped Modes ◽  
Acoustic Waveguide ◽  
Trapped Mode ◽  
Rectangular 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.

Acoustic resonances and trapped modes in pipes and tunnels

2008 ◽  
Vol 605 ◽  
pp. 401-428 ◽  
Author(s):  
STEFAN HEIN ◽  
WERNER KOCH
Keyword(s):  
Cross Sections ◽  
High Speed ◽  
Hard Spheres ◽  
Cutoff Frequency ◽  
Three Dimensional ◽  
Absorbing Boundary Conditions ◽  
Trapped Modes ◽  
Absorbing Boundary ◽  
Complex Scaling Method ◽  
Acoustic Resonances

Acoustic resonances of simple three-dimensional finite-length structures in an infinitely long cylindrical pipe are investigated numerically by solving an eigenvalue problem. To avoid unphysical reflections at the finite grid boundaries placed in the uniform cross-sections of the pipe, perfectly matched layer absorbing boundary conditions are applied in the form of the complex scaling method of atomic and molecular physics. Examples of the structures investigated are sound-hard spheres, cylinders, cavities and closed side branches. Several truly trapped modes with zero radiation loss are identified for frequencies below the first cutoff frequency of the pipe. Such trapped modes can be excited aerodynamically by coherent vortices if the frequency of the shed vortices is close to a resonant frequency. Furthermore, numerical evidence is presented for the existence of isolated embedded trapped modes for annular cavities above the first cutoff frequency and for closed side branches below the first cutoff frequency. As applications of engineering interest, the acoustic resonances are computed for a ball-type valve and around a simple model of a high-speed train in an infinitely long tunnel.

Acoustic resonances and trapped modes in annular plate cascades

2009 ◽  
Vol 628 ◽  
pp. 155-180 ◽  
Author(s):  
WERNER KOCH
Keyword(s):  
Axial Flow ◽  
Radiation Condition ◽  
Absorbing Boundary Conditions ◽  
Radiation Damping ◽  
Resonance Problem ◽  
Trapped Modes ◽  
Mean Flow ◽  
Absorbing Boundary ◽  
Complex Scaling Method ◽  
Acoustic Resonances

As a stepping stone towards understanding acoustic resonances in axial flow compressors, acoustic resonances are computed numerically in fixed single and tandem plate cascades in an infinitely long annular duct. Applying perfectly matched layer absorbing boundary conditions in the form of the complex scaling method of atomic and molecular physics to approximate the radiation condition the resonance problem is transformed into an eigenvalue problem. Of particular interest are resonances with zero radiation damping (trapped modes) or very small radiation damping (nearly trapped modes). Such resonances can be excited by wakes from compressor cascades or struts. If the shedding frequency is sufficiently close to an acoustic resonant frequency, the latter may control the vortex shedding causing high-intensity tonal noise or occasionally even blade failure. All resonances are computed for zero mean flow approximating low-Mach-number flows. The influence of various cascade parameters on the resonant frequencies is studied and, whenever possible, our numerical results are compared with published experimental findings.

Fano resonances in acoustics

2010 ◽  
Vol 664 ◽  
pp. 238-264 ◽  
Author(s):  
STEFAN HEIN ◽  
WERNER KOCH ◽  
LOTHAR NANNEN
Keyword(s):  
Acoustic Waves ◽  
Open Systems ◽  
Absorbing Boundary Conditions ◽  
Circular Cylinders ◽  
Fano Resonances ◽  
Trapped Modes ◽  
Mean Flow ◽  
Scattering Problems ◽  
Complex Scaling Method ◽  
Confined Domains

In contrast to completely open systems, laterally confined domains can sustain localized, truly trapped modes with nominally zero radiation loss. These discrete resonant modes cannot be excited linearly by the continuous propagating duct modes due to symmetry constraints. If the symmetry of the geometry is broken the trapped modes become highly localized quasi-trapped modes which can interfere with the propagating duct modes. The resulting narrowband Fano resonances with resonance and antiresonance features are a generic phenomenon in all scattering problems with multiple resonant pathways. This paper deals with the classical scattering of acoustic waves by various obstacles such as hard-walled single and multiple circular cylinders or rectangular and wedge-like screens in a two-dimensional duct without mean flow. The transmission and reflection coefficients as well as the (complex) resonances are computed numerically by means of the finite-element method in conjunction with two different absorbing boundary conditions, namely the complex scaling method and the Hardy space method. The results exhibit the typical asymmetric Fano line shapes near the trapped-mode resonances if the symmetry of the geometry is broken.

The propagation of very low-frequency waves in ducts in the magnetosphere. Il

1972 ◽  
Vol 329 (1577) ◽  
pp. 219-231 ◽  
Keyword(s):  
Low Frequency ◽  
Angular Spectrum ◽  
Trapped Modes ◽  
Trapped Mode ◽  
Leaky Modes ◽  
Integral Methods ◽  
Barrier Region ◽  
New Type ◽  
Forbidden Region ◽  
Low Frequency Waves

Because of transverse gradients of refractive index, magnetospheric ducts which guide whistlers are not isolated. The whistlers are likely to leak from the ducts through a forbidden region owing to barrier penetration by evanescent waves. This phenomenon is investigated theoretically by using the WKB J approximation and phase integral methods. A new type of mode called a quasi-trapped mode is discussed. It is shown that, if a wave packet is incident on a duct capable of sustaining quasi-trapped modes, certain components of its angular spectrum are selectively trapped. These travel in quasi-trapped modes for considerable distances before leaking from the duct. Expressions are derived for the distance travelled in terms of the width of the duct, the width of the barrier region, and the properties of the medium. A connexion between this type of solution and a solution in terms of leaky modes is discussed.

Despeckling of Sar Images Using Shrinkage of Two-Dimensional Discrete Orthonormal S-Transform

2020 ◽  
pp. 2150023
Author(s):  
Priya R. Kamath ◽  
Kedarnath Senapati ◽  
P. Jidesh
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Relevant Information ◽  
Detection Algorithm ◽  
Two Dimensional ◽  
Sar Images ◽  
S Transform ◽  
Processing Step ◽  
Frequency Components ◽  
Shock Filter

Speckles are inherent to SAR. They hide and undermine several relevant information contained in the SAR images. In this paper, a despeckling algorithm using the shrinkage of two-dimensional discrete orthonormal S-transform (2D-DOST) coefficients in the transform domain along with shock filter is proposed. Also, an attempt has been made as a post-processing step to preserve the edges and other details while removing the speckle. The proposed strategy involves decomposing the SAR image into low and high-frequency components and processing them separately. A shock filter is used to smooth out the small variations in low-frequency components, and the high-frequency components are treated with a shrinkage of 2D-DOST coefficients. The edges, for enhancement, are detected using a ratio-based edge detection algorithm. The proposed method is tested, verified, and compared with some well-known models on C-band and X-band SAR images. A detailed experimental analysis is illustrated.

scholarly journals Tunable characteristics of low-frequency bandgaps in two-dimensional multivibrator phononic crystal plates under prestrain

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hai-Fei Zhu ◽  
Xiao-Wei Sun ◽  
Ting Song ◽  
Xiao-Dong Wen ◽  
Xi-Xuan Liu ◽  
...  
Keyword(s):  
Phononic Crystal ◽  
Real Life ◽  
Low Frequency ◽  
Acoustic Vibration ◽  
Crystal Plate ◽  
Frequency Noise ◽  
Two Dimensional ◽  
The Matrix ◽  
Noise Frequency ◽  
Realtime Control

AbstractIn view of the influence of variability of low-frequency noise frequency on noise prevention in real life, we present a novel two-dimensional tunable phononic crystal plate which is consisted of lead columns deposited in a silicone rubber plate with periodic holes and calculate its bandgap characteristics by finite element method. The low-frequency bandgap mechanism of the designed model is discussed simultaneously. Accordingly, the influence of geometric parameters of the phononic crystal plate on the bandgap characteristics is analyzed and the bandgap adjustability under prestretch strain is further studied. Results show that the new designed phononic crystal plate has lower bandgap starting frequency and wider bandwidth than the traditional single-sided structure, which is due to the coupling between the resonance mode of the scatterer and the long traveling wave in the matrix with the introduction of periodic holes. Applying prestretch strain to the matrix can realize active realtime control of low-frequency bandgap under slight deformation and broaden the low-frequency bandgap, which can be explained as the multiple bands tend to be flattened due to the localization degree of unit cell vibration increases with the rise of prestrain. The presented structure improves the realtime adjustability of sound isolation and vibration reduction frequency for phononic crystal in complex acoustic vibration environments.

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