The theory of the scattering of plane waves in a fluid medium by an isotropic elastic sphere representing a manganese nodule is developed. Scattering cross sections were computed using the theory and the results are presented graphically. The scattering cross section and the reflectivity factor govern the characteristic acoustic signature of the Pacific where manganese nodules are present. Preliminary experimental data for the compressional and shear wave speeds in nodule material is given. This data was used in the scattering computations. Limiting cases of Rayleigh scattering and scattering from fixed rigid and fluid spheres are also shown for comparison. It is shown that the rigidity of the nodules dominates the high frequency response. The problem of the multiple scattering of acoustic waves by randomly distributed nodules on the flat ocean bottom is investigated analytically. The statistical description of nodule deposits is given. The concept of the configurational average is introduced in order to obtain the average scattered response. The size averaging is found to be able to smooth the acoustic response in the high frequency region. The plane wave analysis for the multiple scattering problem is justified by the narrow beam investigation. It shows that the beam effect on the average backscattered field can be neglected in the remote sensing. For a planar distribution of nodules, the average scattered field excited by a normally incident plane wave is verified to be plane waves characterized by coherent reflection and transmission coefficients. The multiple scattering effect is found to be a higher order correction to the average scattered field. For a sparse distribution of nodules, the average scattered field can be well evaluated using the single scattering theory in which the scattering process is also shown to be energy conserved. For a dense distribution of nodules, the radial distribution function is used in the Foldy-Lax hierarchy. The result shows that the pair correlation affects the phase of the second order correction term in the expression for the average scattered field when the higher order statistics are truncated using the quasi crystalline approximation. / Ph. D.

Thesis (S.M.)--Joint Program in Oceanography/Applied Ocean Science and Engineering (Massachusetts Institute of Technology, Dept. of Mechanical Engineering; and the Woods Hole Oceanographic Institution), 2008. / Includes bibliographical references (p. 145-149). / Benthic shells can contribute greatly to the scattering variability of the ocean bottom, particularly at low grazing angles. Among the effects of shell aggregates are increased scattering strength and potential subcritical angle penetration of the seafloor. Sand dollars (Dendraster excentricus) occur commonly in the ocean and have been shown to be significant scatters of sound. In order to understand more fully the scattering mechanisms of these organisms, the scattering from individual sand dollars was studied using several methods. Using an approximation to the Helmholtz-Kirchhoff integral, the Kirchhoff method gives an analytic integral expression to the backscattering from an object. This integral was first solved analytically for a disk and a spherical cap, two high aspect ratio oblate shapes which simplify the shape of an individual sand dollar. A method for solving the Kirchhoff integral numerically was then developed. An exact three dimensional model of a sand dollar test was created from computed tomography scans. The Kirchhoff integral was then solved numerically for this model of the sand dollar. The finite element method, a numerical technique for approximating the solutions to partial differential equations and integral equations, was used to model the scattering from an individual sand dollar as well. COMSOL Multiphysics was used for the implementation of the finite element method. Modeling results were compared with published laboratory experimental data from the free field scattering of both an aluminum disk and a sand dollar. Insight on the scattering mechanisms of individual sand dollar, including elastic behavior and diffraction effects, was gained from these comparisons. / by Gregory C. Dietzen. / S.M.

[Truncated abstract] This thesis presents three different methods to investigate flexural wave propagation and scattering, power flow and transmission efficiencies, and dynamic stress concentration and fatigue failures in structural dynamics. The first method is based on the acoustical wave propagator (AWP) technique, which is the main part described in this thesis. Through the numerical implementation of the AWP, the complete information of the vibrating structure can be obtained including displacement, velocity, acceleration, bending moments, strain and stresses. The AWP technique has been applied to systems consisting of a one-dimensional stepped beam, a two-dimensional thin plate, a thin plate with a sharp change of section, a heterogeneous plate with multiple cylindrical patches, and a Mindlin?s plate with a reinforced rib. For this Mindlin?s plate structure, through the comparison of the results obtained by Mindlin?s thick plate theory and Kirchhoff?s classical thin plate theory, the difference of theoretical predicted results is investigated. As part of these investigations, reflection and transmission coefficients, power flow and transmission efficiencies in a onedimensional stepped beam, and power flow in a two-dimensional circular plate structure, are studied. In particular, this technique has been successfully extended to investigate wave propagation and scattering, and dynamic stress concentration at discontinuities. Potential applications are fatigue failure prediction and damage detection in complex structures. The second method is based on experimental techniques to investigate the structural response under impact loads, which consist of the waveform measuring technique in the time domain by using the WAVEVIEW software, and steady-state measurements by using the Polytec Laser Scanning Vibrometer (PLSV) in the frequency domain. The waveform measuring technique is introduced to obtain the waveform at different locations in the time domain. These experimental results can be used to verify the validity of predicted results obtained by the AWP technique. Furthermore, distributions of dynamic strain and stress in both near-field (close to discontinuities) and far-field regions are investigated for the study of the effects of the discontinuities on reflection and transmission coefficients in a one-dimensional stepped beam structure. Experimental results in the time domain can be easily transferred into those in the frequency domain by the fast Fourier transformation, and compared with those obtained by other researchers. This PLSV technique provides an accurate and efficient tool to investigate mode shape and power flow in some coupled structures, such as a ribbed plate. Through the finite differencing technique, autospectral and spatial of dynamic strain can be obtained. The third method considered uses the travelling wave solution method to solve reflection and transmission coefficients in a one-dimensional stepped beam structure in the time domain. In particular, analytical exact solutions of reflection and transmission coefficients under the given initial-value problem are derived. These analytical solutions together with experimental results can be used to compare with those obtained by the AWP technique.

The effects of vortices on the propagation of acoustic waves are numerous, from simple convection effects to instabilities in the acoustic phenomena, including absorption,<p>reflection and refraction effects. This work focusses on the effects of mean flow<p>vorticity on the acoustic propagation. First, a theoretical background is presented<p>in chapters 2-5. This part contains: (i) the fluid dynamics and thermodynamics<p>relations; (ii) theories of sound generation by turbulent flows; and (iii) operators taken<p>from scientific literature to take into account the vorticity effects on acoustics. Later,<p>a family of scalar operators based on total enthalpy terms are derived to handle mean<p>vorticity effects of arbitrary flows in acoustics (chapter 6). Furthermore, analytical<p>solutions of Pridmore-Brown’s equation are featured considering exponential boundary<p>layers whose profile depend on the acoustic parameters of the problem (chapter 7).<p>Finally, an extension of Pridmore-Brown’s equation is formulated for predicting the<p>acoustic propagation over a locally-reacting liner in presence of a boundary layer of<p>linear velocity profile superimposed to a constant cross flow (chapter 8).<p> / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished