Acoustic Interactions With Submerged Elastic Structures: Acoustic Scattering and Resonances

by Guran, Ardeshir; Ripoche, Jean; Ziegler, F.

• ISBN13: 9789810229641
• ISBN10: 981022964X
• Format: Hardcover
• Copyright: 1996-06-01
• Publisher: World Scientific Pub Co Inc

Summary

"\berall's work in acoustic and electromagnetic scattering has evoked much interest, in the US as well as abroad, because of its possible practical applications, as well as the theoretical understanding. Many collaborators have been inspired by it, and have now contributed to this volume. The book is an excellent contribution to the literature of Acoustics and Wave Propagation. Professor Guran is to be congratulated for organizing and editing this volume." Prof. Hans A Bethe Noble LaureateCornell University, 1996

Table of Contents

Foreword	vii
Hans A. Bethe
Preface	ix
Ardeshir Guran
Jean Ripoche
Franz Ziegler
Contributors	xv
The Resonances: From Nuclear Physics to Underwater Acoustics	1	(14)
Herbert Uberall
Jean Ripoche
Gerard Maze
Jean-Louis Izbicki
Frequency Spectra of Acoustic Vibrations	1	(1)
Level Spectra of Nuclear States	2	(2)
Nuclear Vibrations	4	(1)
Nuclear Excitations: the Breit-Wigner Resonance Formula	5	(1)
Acoustic Resonance Scattering Theory	5	(2)
The Method of Isolation and Identification of Resonances (MIIR)	7	(3)
Bistatic Scattering: Regge Trajectories	10	(3)
Conclusions	13	(1)
References	13	(2)
RST and Peripheral Waves	15	(29)
Naum Veksler
Introduction	15	(1)
Modern State of RST	16	(2)
Modal Resonances and Peripheral Waves	18	(20)
Normal and Peripheral Waves	18	(3)
Eigenfrequencies and Modal Resonances	21	(2)
Modal Resonances of Franz Waves	23	(1)
Modal Resonances With the Minimal Halfwidth	24	(3)
Lamb-Type Peripheral Waves and Whispering Gallery Waves	27	(2)
Hidden Resonances	29	(5)
Helical Peripheral Waves	34	(2)
Acoustic Spectrogram	36	(2)
Conclusions	38	(2)
References	40	(4)
Acoustic Scattering from Internally Loaded Cylindrical Shells	44	(37)
Yueping Guo
Introduction	44	(4)
Scattered Acoustic Field	48	(2)
Shell Displacements	50	(4)
Internal Plate Vibrations	54	(3)
Scattering Form Function	57	(2)
Equivalence of Modal Solution to Wave Decomposition	59	(3)
Contributions Due to Flexural Waves	62	(5)
Effects on Compressional and Shear Waves	67	(3)
Effects of Internal Plate Resonance	70	(3)
Contributions From Bending Moments	73	(3)
Conclusions	76	(2)
Acknowledgements	78	(1)
References	78	(3)
Scattering by Cylindrical Objects at Oblique Incidence	81	(48)
Jean-Marc Conoir
Pascal Rembert
Jean-Louis Izbicki
Introduction	81	(1)
Resonant Scattering Theory	82	(3)
Form Function	82	(2)
Breit-Wigner Approximation	84	(1)
Sommerfeld-Watson Transformation	85	(19)
Transformation of the Modal Series into an Integral	85	(2)
Asymptotic Expansions of the Bessel Function	87	(1)
Reflection and Refraction of a Plane Wave at a Fluid-Fluid Plane Interface	87	(2)
Refraction Angles and Complex Wave Numbers Related to the Surface Waves	89	(1)
Singularity Calculation	90	(1)
Imai Separation	91	(1)
Geometrical waves	91	(1)
Surface waves	92	(1)
Geometrical Wave Contribution	93	(1)
Specular reflected wave	93	(3)
Refracted waves	96	(1)
High Frequency Behavior of the Reflection-Refraction Coefficients	96	(2)
Geometrical Expansion Coefficient	98	(1)
Surface Wave Scattering in Region ξl > ξ	99	(5)
Surface Waves Scattering in Region ξl < ξ	104	(1)
Physical Meaning of Resonances	104	(2)
Relation Between El and kl''	106	(3)
Experimental Results and Comparison	109	(18)
Introduction	109	(1)
Experimental Isolation and Identification of Cylindrical Scatterer Resonances	109	(3)
Experiments at Small Incidence Angle	112	(1)
Case of a solid cylinder	112	(2)
Case of elastic cylindrical shell	114	(3)
Resonance Behavior with the Incidence Angle	117	(1)
Case of a solid cylinder	117	(7)
Case of an elastic cylindrical shell	124	(3)
References	127	(2)
Nonspecular Reflection-Transmission Phenomena of Bounded Beams Described by Inhomogeneous Plane Waves	129	(35)
Oswald Leroy
Complex Critical Angles for the Reflection Coefficient of a Plane Wave	129	(5)
Numerical Example	134	(4)
Water/Steel Interface	134	(4)
Inhomogeneous Plane Wave in Absorptive Media	138	(4)
Reflection and Transmission of Inhomogeneous Plane Waves	142	(3)
Experimental Verification	145	(2)
Bounded Beam Decomposition in Inhomogeneous Plane Waves	147	(5)
Fourier Decomposition	147	(1)
Inhomogeneous Wave Decomposition	148	(4)
Bounded Beam Reflection: Water/Brass	152	(1)
Scattering of Inhomogeneous Plane Waves from a Periodic Rough Surface	153	(9)
References	162	(2)
Reflection and Refraction of the Inhomogeneous Plane Wave	164	(43)
Marc Deschamps
Introduction	164	(1)
The Inhomogeneous Plane Wave	165	(7)
The Complex Wave Vector	166	(1)
The Normalized Bi-vectors	167	(1)
The Complex Polarization Vectors	168	(1)
The Particle Displacement	168	(3)
Complex Angle of Propagation	171	(1)
The Generalized Snell's Laws	172	(2)
Heterogeneity Coefficient and Angle of Refraction	174	(9)
General Case	175	(2)
Homogeneous and Non-Attenuated Incident Wave on Lossless Solid	177	(1)
Homogeneous and Attenuated Incident Wave on Lossless Solid	178	(2)
Evanescent Incident Wave on Lossless Solid	180	(2)
Homogeneous and Non-Attenuated Incident Wave on Lossy Solid	182	(1)
Generation of the Evanescent Plane Wave	183	(2)
Reflection and Refraction at a Single Interface	185	(8)
Theoretical Results	185	(5)
Energy Conservation Laws	190	(1)
Experimental Results	191	(2)
Reflection and Refraction by an Immersed Plate	193	(11)
Theoretical Results	194	(6)
Energy Conservation Laws	200	(2)
Experimental Results	202	(2)
Conclusions	204	(1)
References	204	(3)
Theory of the Acoustic Bounded Beam	207	(35)
Martine Rousseau
Philippe Gatignol
Introduction to the Bounded Beam Theory	207	(1)
The Green Formalism	207	(1)
The Evanescent Plane Wave Formalism	207	(1)
The Fourier Integral Formalism	208	(1)
The Modelisation Choice	208	(1)
Ultrasonic Beam -- Non-Specular Effects Near the Rayleigh Incidence	208	(9)
A Chronological Description	208	(1)
The Incident Beam	209	(2)
The Reflected Beam: The Non-Specular Effects	211	(6)
Ultrasonic Focused Beam - Distortion of the Reflected Caustic	217	(8)
A Chronological Review	217	(1)
Incident Focused Beam	217	(2)
The Reflected Focused Beam - Distortion of the Caustic	219	(6)
Transient Bounded Beam	225	(15)
Chronological Review	225	(1)
The Incident Beam	225	(4)
The Reflected Transient Beam	229	(11)
References	240	(2)
Sound Scattering by a Fluid-Loaded Cylindrical Shell With a Internal Axial Stiffener	242	(33)
Aleksander Klauson
Jaan Metsaveer
Dominique Decultot
Gerard Maze
Jean Ripoche
Introduction	242	(6)
Solution of the Problem	248	(7)
Experimental Details	255	(2)
Numerical and Experimental Results: Steady-State Symmetrical Excitation	257	(5)
Numerical and Experimental Results: Steady-State Excitation	262	(5)
Numerical Results: Pulse Excitation	267	(4)
Experimental Verification	271	(1)
Conclusions	272	(1)
Acknowledgements	273	(1)
References	273	(2)
Interferences in Elastic Plates	275	(35)
Jean-Marc Conoir
Olivier Lenoir
Jean-Louis Izbicki
Introduction	275	(1)
Reflection and Transmission Coefficients of the Plate	276	(4)
Debye Series Expansion	280	(7)
Characteristic Equation of the Plate	287	(2)
Resonance Calculation When sin &thetas; ≤ c1/cL	289	(2)
Crossing of the Dispersion Curves and Interferences	291	(2)
Periodicity of Resonances at Angles &thetas;pq	293	(2)
Interferences Close to the First Critical Angle	295	(1)
Interferences in the Range &thetas;c(L) ≤ &thetas; ≤ &thetas;c(T)	296	(3)
Parametrical Study of Resonances and Interferences	299	(8)
Longitudinal and Transverse Resonances	299	(5)
Physical Interpretation in Term of Interferences	304	(3)
Conclusions	307	(1)
References	308	(2)
Vibrations of Shells Contacting Fluid: Asymptotic Analysis	310	(23)
Michael Levitin
Dmitri Vassiliev
Introduction	310	(1)
Basic Equations	311	(3)
Coordinate System and Dimensionless Parameters	311	(1)
Shell Equations in Vacuum	311	(2)
Fluid Equations	313	(1)
Equations for a Shell Contacting Fluid	313	(1)
Mathematical Statement and General Properties of the Interior Problem	314	(2)
Mathematical Statement of the Interior Problem	314	(1)
Spectral Properties of the Operator Ai	315	(1)
Existence and Uniqueness of the Solution of the Non-homogeneous Problem	316	(1)
Asymptotics of Eigenfrequencies for the Interior Problem	316	(3)
Decomposition of the Spectrum into Three Series for a Shell of Revolution	316	(1)
Asymptotic Formulae for Tangential and Fluid Eigenfrequencies for a Shell of Revolution	317	(1)
Asymptotic Formulae for Flexural Eigenfrequencies for a Shell of Revolution	318	(1)
Asymptotic Formulae for Eigenfrequencies for a Shell of an Arbitrary Shape	318	(1)
Mathematical Statement and General Properties of the Exterior Problem	319	(5)
L2-Spectrum of the Exterior Problem	319	(1)
Meromorphic Continuation of the Resolvent and Scattering Frequencies	320	(1)
Radiation Conditions	321	(3)
Asymptotics of Scattering Frequencies of the Exterior Problem	324	(1)
Fluid and Tangential Scattering Frequencies	324	(1)
Flexural Scattering Frequencies	324	(1)
Resonance Phenomena	325	(4)
Statement of the Problem	325	(1)
Iteration Process and Asymptotic Expansion in the Absence of Tangential Eigenfrequencies	325	(2)
Asymptotic Expansion in the Vicinity of a Tangential Eigenfrequency	327	(1)
Interpretation of the Results	328	(1)
Effect of Fluid Viscosity	329	(2)
Statement of the Problem	329	(1)
Effect of Viscosity on Eigenfrequencies	330	(1)
Acknowledgements	331	(1)
References	331	(2)
Program of the Symposium in Honor of Professor Herbert Uberall	333	(1)
Subject Index	334	(6)
Author Index	340