Wave propagation in an elastically supported string with point‐wise defects: gap‐band and pass‐band effects

Глушков, Е. В.; Glushkova, Natalia; Wauer, Jörg

doi:10.1002/zamm.201000039

Cited by 17 publications

(16 citation statements)

References 18 publications

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“…Wave phenomena in periodic structures are intensively explored during last years [1][2][3][4]. The extensive bibliography is represented in [1] for example.…”

Section: Introductionmentioning

confidence: 99%

The Location of Pass and Stop Bands of an Infinite Periodic Structure Versus the Eigenfrequencies of Its Finite Segment Consisting of Several “Periodicity Cells”

Filippenko¹

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…Wave phenomena in periodic structures are intensively explored during last years [1][2][3][4]. The extensive bibliography is represented in [1] for example.…”

Section: Introductionmentioning

confidence: 99%

The Location of Pass and Stop Bands of an Infinite Periodic Structure Versus the Eigenfrequencies of Its Finite Segment Consisting of Several “Periodicity Cells”

Filippenko¹

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…It is significant that such transmission peak patterns, as well as the patterns of nearly real pole groups, are inherent to a wide variety of physically different 1D waveguides. 3,[8][9][10][11][12] As M increases, the peaks tightly fill in restricted frequency intervals forming pass bands inside wider gap bands in compliance with the Bloch-Floquet theory.…”

Section: Introductionmentioning

confidence: 65%

“…The derivation and analysis of the string solution, as well as the meaning of defect parameters, are particularized in Ref. 12. The frequency spectrum wðx; xÞ of vertical spring oscillation also has poles in the x-plane.…”

Section: Multiple Poles and Resonant Pass Peaksmentioning

confidence: 99%

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Resonance blocking and passing effects in two-dimensional elastic waveguides with obstacles

Глушков

Glushkova

Golub

et al. 2011

The Journal of the Acoustical Society of America

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Resonance localization of wave energy in two-dimensional (2D) waveguides with obstacles, known as a trapped mode effect, results in blocking of wave propagation. This effect is closely connected with the allocation of natural resonance poles in the complex frequency plane, which are in fact the spectral points of the related boundary value problem. With several obstacles the number of poles increases in parallel with the number of defects. The location of the poles in the complex frequency plane depends on the defect's relative position, but the gaps of transmission coefficient plots generally remain in the same frequency ranges as for every single obstacle separately. This property gives a possibility to extend gap bands by a properly selected combination of various scatterers. On the other hand, a resonance wave passing in narrow bands associated with the poles is also observed. Thus, while a resonance response of a single obstacle works as a blocker, the waveguide with several obstacles becomes opened in narrow vicinities of nearly real spectral poles, just as it is known for one-dimensional (1D) waveguides with a finite number of periodic scatterers. In the present paper the blocking and passing effects are analyzed based on a semi-analytical model for wave propagation in a 2D elastic layer with cracks or rigid inclusions.

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“…More details may be found in Refs. [1,2] and in the papers cited therein. The first of these papers discusses the resonance phenomena in an elastically-supported string with pointwise obstacles (1D waveguide, Fig.…”

Section: Introductionmentioning

confidence: 97%

Spectral points and stop-pass effects in waveguides with obstacles

Глушков

Glushkova

Golub

et al. 2012

2012 International Conference on Mathematical Methods in Electromagnetic Theory

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The blocking and passing effects are analyzed and discussed based on integralequation mathematical models for elastic waveguides with different nature obstacles. Since the mathematical background of various wave phenomena is, generally, the same, the results obtained should be of interest for electromagnetic and coupled piezo-elastic wave propagation as well. The resonance effects take place in the course of guided wave diffraction by local obstacles. These phenomena, which are also known as trapping-mode effects, are usually accompanied by a sharp stopping of the wave energy flow along the waveguide and, consequently, in deep and narrow gaps in the frequency plots of transmission coefficients. Those effects are closely connected with the allocation of nearly real natural frequencies (resonance poles) in the complex frequency plane, which are, in fact, the spectral points of the related boundary value problems. With several obstacles, the number of such poles increases in parallel with the number of defects. On the other hand, a resonance wave passing in narrow bands associated with the poles is also observed. Thus, while a resonance response of a single obstacle in a two-dimensional (2D) waveguide works as a blocker, the waveguide with several obstacles becomes opened in narrow vicinities of nearly real spectral poles, just as it is known for one-dimensional (1D) waveguides with a finite number of scatterers.

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Wave propagation in an elastically supported string with point‐wise defects: gap‐band and pass‐band effects

Cited by 17 publications

References 18 publications

The Location of Pass and Stop Bands of an Infinite Periodic Structure Versus the Eigenfrequencies of Its Finite Segment Consisting of Several “Periodicity Cells”

The Location of Pass and Stop Bands of an Infinite Periodic Structure Versus the Eigenfrequencies of Its Finite Segment Consisting of Several “Periodicity Cells”

Resonance blocking and passing effects in two-dimensional elastic waveguides with obstacles

Spectral points and stop-pass effects in waveguides with obstacles

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