Identification of the acoustic resonances of absorbing cylinders using phase gradient and Argand diagram methods
Identifieur interne : 000877 ( Istex/Corpus ); précédent : 000876; suivant : 000878Identification of the acoustic resonances of absorbing cylinders using phase gradient and Argand diagram methods
Auteurs : Hervé Franklin ; Jean-Marc Conoir ; Jean-Louis IzbickiSource :
- Wave Motion [ 0165-2125 ] ; 2001.
Abstract
The properties of the acoustic resonances of a submerged absorbing elastic cylinder are investigated with the help of a two-channel scattering resonance formalism. In the elastic channel, different transition terms describing the resonance properties are compared. The scattering phase and its derivative with respect to the frequency are also studied thoroughly. Approximate formulae, involving different resonance widths, are given for the transition terms, the phase and its derivative. Argand diagrams of the transition terms are provided, summarising the characteristic quantities of the absorption phenomenon, i.e. the absorption coefficient, the phase and the resonance widths.
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DOI: 10.1016/S0165-2125(01)00073-7
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<front><div type="abstract" xml:lang="en">The properties of the acoustic resonances of a submerged absorbing elastic cylinder are investigated with the help of a two-channel scattering resonance formalism. In the elastic channel, different transition terms describing the resonance properties are compared. The scattering phase and its derivative with respect to the frequency are also studied thoroughly. Approximate formulae, involving different resonance widths, are given for the transition terms, the phase and its derivative. Argand diagrams of the transition terms are provided, summarising the characteristic quantities of the absorption phenomenon, i.e. the absorption coefficient, the phase and the resonance widths.</div>
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<notesStmt><note type="content">Fig. 1: Functions ∣Te(x)∣2 (solid line) and ∣Ta(x)∣2 (dotted line) plotted versus frequency x for mode n=1.</note>
<note type="content">Fig. 2: Exact (solid line) and approximate (dotted line) functions ∣Te(x)∣2 plotted versus frequency x for resonances (1,3) and (1,4).</note>
<note type="content">Fig. 3: Exact (solid line) and approximate (dotted line) functions ∣ T ̄e(x)∣2 plotted versus frequency x for resonances (1,3) and (1,4).</note>
<note type="content">Fig. 4: Exact (solid line) and approximate (dotted line) function ∣TeR(x)∣2 plotted versus frequency x for resonances (1,3) and (1,4).</note>
<note type="content">Fig. 5: Absorbing phase δ(x) (solid line) and nonabsorbing phase δel(x) (dotted line) plotted versus frequency x for mode n=1.</note>
<note type="content">Fig. 6: Absorbing phase δ(x) plotted versus frequency x for resonances (1,3) and (1,4): exact (solid line); Eq. (26) in Fig. 6(a) and Eq. (30) in Fig. 6(b) (dotted line); Eq. (32) (dashed line).</note>
<note type="content">Fig. 7: Exact phase derivative dδ(x)/dx plotted versus frequency x for mode n=1.</note>
<note type="content">Fig. 8: Argand diagrams of resonance (1,4) related to the transition terms Te(x) (inner circle) and T ̄e(x) (outer circle).</note>
<note type="content">Fig. 9: Argand diagrams of resonance (1,3) related to the transition terms Te(x) (circle) and T ̄e(x) (arc of circle).</note>
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<head><ce:title>Identification of the acoustic resonances of absorbing cylinders using phase gradient and Argand diagram methods</ce:title>
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<ce:abstract-sec><ce:simple-para>The properties of the acoustic resonances of a submerged absorbing elastic cylinder are investigated with the help of a two-channel scattering resonance formalism. In the elastic channel, different transition terms describing the resonance properties are compared. The scattering phase and its derivative with respect to the frequency are also studied thoroughly. Approximate formulae, involving different resonance widths, are given for the transition terms, the phase and its derivative. Argand diagrams of the transition terms are provided, summarising the characteristic quantities of the absorption phenomenon, i.e. the absorption coefficient, the phase and the resonance widths.</ce:simple-para>
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<abstract lang="en">The properties of the acoustic resonances of a submerged absorbing elastic cylinder are investigated with the help of a two-channel scattering resonance formalism. In the elastic channel, different transition terms describing the resonance properties are compared. The scattering phase and its derivative with respect to the frequency are also studied thoroughly. Approximate formulae, involving different resonance widths, are given for the transition terms, the phase and its derivative. Argand diagrams of the transition terms are provided, summarising the characteristic quantities of the absorption phenomenon, i.e. the absorption coefficient, the phase and the resonance widths.</abstract>
<note type="content">Fig. 1: Functions ∣Te(x)∣2 (solid line) and ∣Ta(x)∣2 (dotted line) plotted versus frequency x for mode n=1.</note>
<note type="content">Fig. 2: Exact (solid line) and approximate (dotted line) functions ∣Te(x)∣2 plotted versus frequency x for resonances (1,3) and (1,4).</note>
<note type="content">Fig. 3: Exact (solid line) and approximate (dotted line) functions ∣ T ̄e(x)∣2 plotted versus frequency x for resonances (1,3) and (1,4).</note>
<note type="content">Fig. 4: Exact (solid line) and approximate (dotted line) function ∣TeR(x)∣2 plotted versus frequency x for resonances (1,3) and (1,4).</note>
<note type="content">Fig. 5: Absorbing phase δ(x) (solid line) and nonabsorbing phase δel(x) (dotted line) plotted versus frequency x for mode n=1.</note>
<note type="content">Fig. 6: Absorbing phase δ(x) plotted versus frequency x for resonances (1,3) and (1,4): exact (solid line); Eq. (26) in Fig. 6(a) and Eq. (30) in Fig. 6(b) (dotted line); Eq. (32) (dashed line).</note>
<note type="content">Fig. 7: Exact phase derivative dδ(x)/dx plotted versus frequency x for mode n=1.</note>
<note type="content">Fig. 8: Argand diagrams of resonance (1,4) related to the transition terms Te(x) (inner circle) and T ̄e(x) (outer circle).</note>
<note type="content">Fig. 9: Argand diagrams of resonance (1,3) related to the transition terms Te(x) (circle) and T ̄e(x) (arc of circle).</note>
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