Acoustic scattering from an elastic plate reinforced with an infinite number of periodic ribs

A thin elastic plate of finite width is irradiated by time-harmonic acoustic waves. The fluid is assumed light compared with the plate mass, and the forcing term is of sufficient amplitude to necessitate the inclusion of a nonlinear term (due to mid-plane stretching) in the plate equation. The order-one scattered field is determined by the method of multiple scales when the forcing frequency approaches a free oscillation frequency (eigenfrequency) of the plate. This solution is shown to agree with previous work, for the linear problem, and can be multivalued for particular values of the plate-fluid parameters. The scattered wave may also exhibit jumps in its amplitude and phase angle as it varies with frequency, incident-wave angle or incident-wave amplitude. The non-linear term further allows the possibility of secondary and combination resonances. These are investigated and the scattered field is shown to contain terms of different frequencies to those of the incident waves. Multivalued solutions and the associated jump phenomenon are again found for these resonant cases.

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FRACTAL TWO-LEVEL FINITE ELEMENT MESH FOR ACOUSTIC SCATTERING PROBLEMS

Journal of Computational Acoustics ◽

10.1142/s0218396x03001791 ◽

2003 ◽

Vol 11 (01) ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

A. Y. T. LEUNG ◽

G. R. WU ◽

W. F. ZHONG

Keyword(s):

Finite Element ◽

Infinite Number ◽

Acoustic Waves ◽

Mass Matrix ◽

Acoustic Scattering ◽

Finite Element Mesh ◽

Element Mesh ◽

Exterior Region ◽

Number Of Layers ◽

Hankel Functions

The problems of acoustic waves scattered by scatterer immersed in unbounded domain is an essential ingredient in the study of acoustic-structure interaction. In this paper the problems of acoustic scattering in an infinite exterior region are investigated by using a fractal two-level finite element mesh with self-similar layers in the media which encloses the conventional finite element mesh for the cavity. The similarity ratio is bigger than one so that the fractal mesh extends to infinity. Because of the self-similarity, the equivalent stiffness (mass) matrix of one layer is proportional to the others. By means of the Hankel functions automatically satisfying Sommerfeld's radiation conditions at infinity, the different unknown nodal pressures on different layers are transformed to some common unknowns of the Hankel coefficients. The set of infinite number of unknowns of nodal pressure is reduced to the set of finite number of Hankel's coefficients. All layers have the same matrix dimension after the transformation and the respective matrices of each layer are summed. Due to the proportionality, the infinite number of layers can be summed in closed form as the entries of each matrix are in geometric series. That is, processing one layer is enough to virtually represent a set of infinite number of layers covering an infinity domain. No new elements are created. Numerical examples show that this method is efficient and accurate in solving unbounded acoustic problems.

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Acoustic scattering by a finite nonlinear elastic plate - II. Coupled primary and secondary resonances

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1988.0082 ◽

1988 ◽

Vol 418 (1854) ◽

pp. 247-260 ◽

Cited By ~ 4

Keyword(s):

Elastic Plate ◽

Acoustic Scattering ◽

Sound Field ◽

Thin Elastic Plate ◽

Inviscid Fluid ◽

Sound Waves ◽

Secondary Resonances ◽

Near Resonance ◽

Plane Sound ◽

Scattered Fields

A finite thin elastic plate is set in an infinite rigid baffle and the whole is immersed in a compressible inviscid fluid. Plane sound waves are incident on the elastic plate, and the fluid is assumed light compared with the plate density. Nonlinear terms in the plate equation have previously been found to markedly alter the scattered sound field near resonance; and it is shown in this paper that in-plane tension may result in simultaneous primary and secondary resonances. This coincidence of resonances gives rise to two scattered fields, one oscillating at the acoustic forcing frequency and the other at three times or one third of this frequency. Both terms have amplitudes which are of the same order as this incident wave and so under certain circumstances much of the incident energy is found to be scattered back off the plate at the secondary frequency.

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Acoustic scattering on an elastic plate described by the Timoshenko model: Contact conditions and uniqueness of the solution

The Journal of the Acoustical Society of America ◽

10.1121/1.421195 ◽

1998 ◽

Vol 103 (2) ◽

pp. 673-682 ◽

Cited By ~ 5

Author(s):

I. V. Andronov ◽

B. P. Belinskiy

Keyword(s):

Elastic Plate ◽

Acoustic Scattering ◽

Timoshenko Model ◽

Contact Conditions ◽

Uniqueness Of The Solution

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Acoustic scattering by a narrow crack in an elastic plate

Wave Motion ◽

10.1016/0165-2125(96)00009-1 ◽

1996 ◽

Vol 24 (1) ◽

pp. 101-115 ◽

Cited By ~ 10

Author(s):

Ivan Andronov ◽

Boris P. Belinskiy ◽

Jerald P. Dauer

Keyword(s):

Elastic Plate ◽

Acoustic Scattering

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Acoustic scattering by a finite elastic plate connecting two fluid-loaded parallel plates

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1993.0154 ◽

1993 ◽

Vol 443 (1918) ◽

pp. 429-444 ◽

Cited By ~ 1

Keyword(s):

Elastic Plate ◽

Acoustic Scattering ◽

Elastic Plates ◽

Parallel Plates ◽

Fluid Loading ◽

Heavy Fluid ◽

Low Frequencies ◽

Plane Sound ◽

Two Fluid ◽

Good Agreement

A plane sound wave is incident upon two infinite parallel elastic plates which are connected by a finite elastic plate. All three plates support compressional and bending motion, and interact with any compressible fluid with which they are in contact. A method, which can be applied to obtain numerical results, for calculating the sound scattered by the connecting plate is presented. In the absence of fluid between the plates an approximate solution, valid for low frequencies and heavy fluid-loading on the upper plate, has been derived which exhibits good agreement with results obtained numerically.

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