Resonance Acoustic Spectroscopy deals with the analysis ofwaves generated in an elastic body by a plane harmonicacoustic wave. It is the first monograph to treat newanalytical and experimental methods for the investigation ofthe excitation, propagation and re-radiation of elasticwaves in solid, thick-walled and thin-walled elasticscatterers.The material is presented systematically,comprising the formulation of the problem, method ofsolution, algorithm, computation and analysis. A largenumber of computational results are given in the form ofmodal resonances, form functions, dispersion curves…mehr
Resonance Acoustic Spectroscopy deals with the analysis ofwaves generated in an elastic body by a plane harmonicacoustic wave. It is the first monograph to treat newanalytical and experimental methods for the investigation ofthe excitation, propagation and re-radiation of elasticwaves in solid, thick-walled and thin-walled elasticscatterers.The material is presented systematically,comprising the formulation of the problem, method ofsolution, algorithm, computation and analysis. A largenumber of computational results are given in the form ofmodal resonances, form functions, dispersion curves andacoustic spectrograms. Particular attention is paid to theinterpretation of the solutions.
1 Scattering of an Obliquely Incident Plane Acoustic Wave by a Circular-Cylindrical Shell of Infinite Extent.- 1.1 Formulation of the Problem and Its Solution in Series Form.- 1.2 Numerical Results.- 2 Resonance Scattering by Elastic Bodies of Cylindrical Shape.- 2.1 Scattering by a Solid Elastic Cylinder.- 2.2 Numerical Results for Scattering by a Solid Elastic Cylinder.- 2.3 Scattering by a Circular-Cylindrical Shell.- 2.4 Numerical Results for the Problem of a Plane Acoustic Pressure Wave Scattered by a Circular-Cylindrical Shell.- 3 Application of the Resonance Scattering Theory to Problems of Acoustic Wave Scattering by Elastic Spheres.- 3.1 Scattering by a Solid Elastic Sphere.- 3.2 Numerical Results for Scattering by a Solid Elastic Sphere.- 3.3 Scattering by an Elastic Spherical Shell.- 3.4 Numerical Results for Scattering by Thick-Walled Spherical Shells.- 4 Synthesis of the Backscattering Form Function for a Solid Elastic Sphere Using the Sommerfeld-Watson Transformation.- 4.1 Approximate Formula for the Description of the Form Function.- 4.2 Features of the Rayleigh Wave.- 4.3 Synthesis of the Form Function.- 4.4 Comparison with Experiment.- 5 Resonance Isolation and Identification Method.- 5.1 The Essence of the Method.- 5.2 Results.- 5.3 Acoustic Spectrogram.- 5.4 Resonances of Guided Waves.- 6 Pulsed Resonance Identification Method.- 6.1 The Essence of the Method.- 6.2 Results.- 7 Peripheral Waves in the Scattering by Elastic Cylinders and Spheres.- 7.1 Scattering from an Elastic Cylinder.- 7.2 Scattering from a Solid Elastic Sphere.- 8 Analysis of Peripheral Waves via Backscattering by Circular-Cylindrical Shells.- 8.1 Introductory Remarks.- 8.2 Model Problem: Lamb-Type Waves in a Plane "Dry" Layer.- 8.3 Application of the Resonance ScatteringTheory.- 8.4 Form Function Analysis.- 8.5 Phase Velocities.- 8.6 Asymptotic Formula for Resonance Frequenciea.- 9 Analysis and Synthesis of the Backscattered Acoustic Pressure from a Circular-Cylindrical Shell.- 9.1 Analysis of the Acoustic Pressure Scattered by the Shell.- 9.2 Synthesis of the Approximate Formula for the Backscattering Form Function.- 9.3 Discussion.- 10 Peripheral Waves in the Scattering by Spherical Shells.- 10.1 Form Function and Isolated Modal Resonances.- 10.2 Dispersion Curves.- 10.3 Approximation of Resonance Positions.- 10.4 Hidden Resonances.- 11 Peripheral Waves in the Scattering of a Plane Acoustic Wave Obliquely Incident on a Solid Elastic Cylinder.- 11.1 Form Function.- 11.2 Modal Resonances.- 11.3 Dispersion Curves of the Phase Velocities.- 12 Analysis of Peripheral Waves in the Scattering of a Plane Acoustic Wave Obliquely Incident on a Circular-Cylindrical Shell.- 12.1 Form Function Analysis.- 12.2 Modal Resonances.- 12.3 Phase Velocities of Peripheral Waves.- 12.4 Estimation of the Resonance Frequency Positions.- 13 On the Causes of Possible Errors in the Solution of Scattering Problems.- 13.1 Application of a Model Outside its Region of Validity.- 13.2 Application of the Procedure Outside its Region of Validity.- 13.3 Boundedness of the Frequency Domain.- 13.4 Extremely Large Computation Steps.- 13.5 Series Truncation at a Small Number of Terms.- 13.6 Ordinary Precision.- 13.7 Errors in Interpretation.- 14 Estimation of the Shell Thickness from the Form Function.- 14.1 Form Function Structure in the Domain of the First Resonances of the S0 Wave.- 14.2 Estimation of the Shell Thickness.- 14.3 Commentary.- References.
1 Scattering of an Obliquely Incident Plane Acoustic Wave by a Circular-Cylindrical Shell of Infinite Extent.- 1.1 Formulation of the Problem and Its Solution in Series Form.- 1.2 Numerical Results.- 2 Resonance Scattering by Elastic Bodies of Cylindrical Shape.- 2.1 Scattering by a Solid Elastic Cylinder.- 2.2 Numerical Results for Scattering by a Solid Elastic Cylinder.- 2.3 Scattering by a Circular-Cylindrical Shell.- 2.4 Numerical Results for the Problem of a Plane Acoustic Pressure Wave Scattered by a Circular-Cylindrical Shell.- 3 Application of the Resonance Scattering Theory to Problems of Acoustic Wave Scattering by Elastic Spheres.- 3.1 Scattering by a Solid Elastic Sphere.- 3.2 Numerical Results for Scattering by a Solid Elastic Sphere.- 3.3 Scattering by an Elastic Spherical Shell.- 3.4 Numerical Results for Scattering by Thick-Walled Spherical Shells.- 4 Synthesis of the Backscattering Form Function for a Solid Elastic Sphere Using the Sommerfeld-Watson Transformation.- 4.1 Approximate Formula for the Description of the Form Function.- 4.2 Features of the Rayleigh Wave.- 4.3 Synthesis of the Form Function.- 4.4 Comparison with Experiment.- 5 Resonance Isolation and Identification Method.- 5.1 The Essence of the Method.- 5.2 Results.- 5.3 Acoustic Spectrogram.- 5.4 Resonances of Guided Waves.- 6 Pulsed Resonance Identification Method.- 6.1 The Essence of the Method.- 6.2 Results.- 7 Peripheral Waves in the Scattering by Elastic Cylinders and Spheres.- 7.1 Scattering from an Elastic Cylinder.- 7.2 Scattering from a Solid Elastic Sphere.- 8 Analysis of Peripheral Waves via Backscattering by Circular-Cylindrical Shells.- 8.1 Introductory Remarks.- 8.2 Model Problem: Lamb-Type Waves in a Plane "Dry" Layer.- 8.3 Application of the Resonance ScatteringTheory.- 8.4 Form Function Analysis.- 8.5 Phase Velocities.- 8.6 Asymptotic Formula for Resonance Frequenciea.- 9 Analysis and Synthesis of the Backscattered Acoustic Pressure from a Circular-Cylindrical Shell.- 9.1 Analysis of the Acoustic Pressure Scattered by the Shell.- 9.2 Synthesis of the Approximate Formula for the Backscattering Form Function.- 9.3 Discussion.- 10 Peripheral Waves in the Scattering by Spherical Shells.- 10.1 Form Function and Isolated Modal Resonances.- 10.2 Dispersion Curves.- 10.3 Approximation of Resonance Positions.- 10.4 Hidden Resonances.- 11 Peripheral Waves in the Scattering of a Plane Acoustic Wave Obliquely Incident on a Solid Elastic Cylinder.- 11.1 Form Function.- 11.2 Modal Resonances.- 11.3 Dispersion Curves of the Phase Velocities.- 12 Analysis of Peripheral Waves in the Scattering of a Plane Acoustic Wave Obliquely Incident on a Circular-Cylindrical Shell.- 12.1 Form Function Analysis.- 12.2 Modal Resonances.- 12.3 Phase Velocities of Peripheral Waves.- 12.4 Estimation of the Resonance Frequency Positions.- 13 On the Causes of Possible Errors in the Solution of Scattering Problems.- 13.1 Application of a Model Outside its Region of Validity.- 13.2 Application of the Procedure Outside its Region of Validity.- 13.3 Boundedness of the Frequency Domain.- 13.4 Extremely Large Computation Steps.- 13.5 Series Truncation at a Small Number of Terms.- 13.6 Ordinary Precision.- 13.7 Errors in Interpretation.- 14 Estimation of the Shell Thickness from the Form Function.- 14.1 Form Function Structure in the Domain of the First Resonances of the S0 Wave.- 14.2 Estimation of the Shell Thickness.- 14.3 Commentary.- References.
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