Acoustic Interactions with Submerged Elastic Structures

The following sections are included:

• Foreword

• Preface

• Contributors

• Contents

Atomic nuclei will resonate when hit by incident electrons, photons or nuclear particles. Known as “Breit-Wigner resonances”, these phenomena are described by an elegant mathematical formalism. Since physical concepts are similar in many different applications, we have been able to transfer this formalism to macroscopic dimensions: the resonances of submerged elastic objects excited by incident acoustic waves; and we have developed an experimental method to isolate and identify these resonances.

The steady-state scattering problems of an acoustic wave scattering by elastic bodies of spherical and cylindrical shape are discussed. The recently proposed approaches in the Resonance Scattering Theory (RST) are briefly considered. The results of the RST application for computation of the resonant components of partial modes are presented. The main attention is given to the analysis of the physical mechanism of the scattering process.

This paper studies sound scattering from cylindrical shells with internal structures. Discussed in detail are the effects of internal structural loading on the interactions between sound and the shell and on the scattered acoustic field. Main results of recent research on this topic are recovered and analyzed by examining a canonical problem where the internal structure is represented by an elastic plate attached to a shell along its axial direction, modeling decks in real underwater vehicles. This canonical problem also reveals features associated with oblique incidence, which do not seem to have been previously studied. Standard method for solving such coupled problems is used to derive solutions in terms of coupling forces and bending moments at the attachment locations, which themselves are determined by kinematic and dynamic balances between the shell and the internal plate, and hence, characterize the sound/shell/plate interactions. The scattered acoustic field is examined to identify dominant features in the scattering process and to reveal the effects of different attachment conditions on the far field scattering.

This paper deals with an extension of the Resonant Scattering Theory to the acoustic scattering by elastic cylinders at oblique incidence. The Sommerfeld-Watson transformation is developed with particular care. We show that resonances are due to the phase matching of helical surface waves which propagate around the cylinder. A relation is established between diffraction and attenuation coefficients related to the helical surface waves. Some results concerning the resonances due to helical surface waves of “circumferential” and “guided” type are discussed.

Considering the analytical expression for the reflection- or transmission-coefficient of ultrasonic waves on plates, we find for certain angles of incidence that the numerator or the denominator becomes zero. Those angles are never real, but complex. The physical interpretation of a complex incident angle is given by the introduction of inhomogeneous plane waves. We give a fundamental study of the propagation in absorptive media and discuss the reflection and transmission on flat and rough surfaces. We also introduce the decomposition of bounded acoustic beams into inhomogeneous plane waves propagating all together in the same direction.

This paper reviews recent work on the reflection and the refraction of a harmonic inhomogeneous plane wave on single plane interfaces as well as immersed plates. Generalized Snell's laws at a plane interface are discussed. As in optics, associated with a heterogeneity coefficient, both refractive and vanishing indices may be used. The reflection and transmission coefficients are then obtained. A bulk inhomogeneous (or evanescent) plane wave is experimentally generated in a fluid by transmission through a prism made of a lossy solid. Theoretical results are compared with the ensuing experimental data. The most important result is the observation of reflection and transmission coefficients greater than unity. This effect agrees with the inhomogeneous plane wave theory yielding the energy balance. It is clearly shown that only a peculiar refraction, corresponding to an angle of refraction greater than 90°, can explain the Rayleigh peak both measured and predicted. Concerning the immersed plate, a similar behavior appears close to the Lamb angles, where the reflection and the transmission coefficients of the plate tend to infinity.

Ultrasonic experiments devoted to the non-destructive evaluation or other specific applications use acoustic emitters, focalized or not, pulsed or continuous. When the width of these emitters is of the same order as the observation distance - near field - the plane wave model is not appropriate to describe the acoustic perturbations. So, it is then necessary to introduce a more suitable model based upon a bounded beam theory. In this chapter, some of the most typical effects due to these non-purely-geometrical aspects are exhibited using the Fourier formalism.

A theoretical and experimental study of a submerged axially stiffened cylindrical shell under the action of the acoustic load is presented. The shell is excited by a plane wave of normal incidence. An analytical solution of the sound scattering problem is derived by the modal expansion using the unstiffened cylindrical shell modes. The coupling forces are determined from the constraint conditions in the structural joints, and the sound pressure as a superposition of the empty shell field and of that radiated by the coupling forces. Dynamic interaction of the rib and the shell brings about considerable modifications in the scattered sound pressure field of the structure. On the basis of the frequency and time response analysis the stiffener-borne wave generation mechanisms are shown. For a steady-state excitation all observed pressure field resonances can be classified according to the coupling force components prevailing in their generation. The normal component of the coupling force and the coupling moment generate a subsonic flexural wave. The flexural vibrations of the shell contribute to backscattered sound pressure essentially through the structural joints. The transversal coupling forces cause strongly radiating membrane type vibrations in the shell. Experimental verification of the results confirm the theoretical predictions.

This paper deals with the acoustic scattering by an elastic plate. The Debye series expansion of the reflection and transmission coefficients allows to rewrite these in the form of multiple scattering of longitudinal and transverse waves propagating inside the plate. The characteristic equation is then written in a new way, which uses the local reflection-refraction coefficients linked to the two interfaces of the plate, and to the acoustical trajectories of the longitudinal and transverse waves inside the plate. Then, we show that there is a countable infinity of angles, for which the dispersion curves of the symmetric and antisymmetric Lamb waves are crossing. At these angles, there is a periodicity for the distribution of resonances, and when the dispersion curves are crossing, the resonances result from interferences between all the longitudinal and transverse waves refracted in the plate. Different cases of interferences due to the transverse waves are also considered close to the first critical angle and between the first and the second critical angles. The behavior of the resonances is studied, in the case of small angles of incidence, versus the longitudinal and transverse velocites of the waves in the plate, and we show that resonances are due to the phase matching of longitudinal or transverse reflected waves inside the plate. The resonances are thus explained in term of interferences.

We consider free and forced harmonic vibrations of a thin elastic shell filled with or immersed into fluid. We construct the asymptotics of the eigenfrequencies and scattering frequencies in the problems of free vibrations, and of the solutions of non-homogeneous problems, using the relative shell thickness as the main asymptotic parameter.

The following sections are included:

• Program of the Symposium in Honor of Professor Herbert Überall

• Subject Index

• Author Index

• About the Editors