Resonance Acoustic Spectroscopy

ISBN-13: 9783642847974 / Angielski / Miękka / 2014 / 282 str.

Naum D. Veksler

Opis

Resonance Acoustic Spectroscopy deals with the analysis of waves generated in an elastic body by a plane harmonic acoustic wave. It is the first monograph to treat new analytical and experimental methods for the investigation of the excitation, propagation and re-radiation of elastic waves in solid, thick-walled and thin-walled elastic scatterers.The material is presented systematically, comprising the formulation of the problem, method of solution, algorithm, computation and analysis. A large number of computational results are given in the form of modal resonances, form functions, dispersion curves and acoustic spectrograms. Particular attention is paid to the interpretation of the solutions.

Spis treści

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.- 5.2.1 Solid Elastic Cylinder.- 5.2.2 Thick-Walled Cylindrical Shell.- 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.- 6.2.1 Solid Elastic Cylinder.- 6.2.2 Cylindrical Shells.- 6.2.3 Spherical Shells.- 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 Scattering Theory.- 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.- 9.2.1 The Specularly Reflected Wave and the Waves Refracted in a Thin Layer.- 9.2.2 The S0 Wave.- 9.2.3 The A Wave.- 9.3 Discussion.- 10 Peripheral Waves in the Scattering by Spherical Shells.- 10.1 Form Function and Isolated Modal Resonances.- 10.1.1 The A Wave.- 10.1.2 The S0 Wave.- 10.1.3 The A1 Wave.- 10.1.4 The S1 Wave.- 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.- 13.7.1 Indirect Methods of Finding the Resonance Frequencies.- 13.7.2 Inadequate Choice of the Background.- 13.7.3 Families of Resonances with Equal Cutoff Frequencies.- 13.7.4 Superposition of Resonances with Low Q Factor.- 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.