TECHNIQUES FOR NUMERICALLY EVALUATING THE FORMULAS DESCRIBING MONOSTATIC REFLECTION OF ACOUSTIC WAVES BY ELASTIC SPHERES.
NAVAL RESEARCH LAB WASHINGTON D C
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Numerical methods are described by which the theoretical formulas specifying the acoustic field resulting from scattering of an acoustic wave by an elastic sphere may be evaluated. They are restricted to the case of monostatic reflection of a plane harmonic wave incident upon the elastic sphere - the sphere being immersed in a uniform homogeneous fluid, the acoustic properties of which are assumed to be the same at all frequencies. Methods of calculating reflection form-functions as a function of sphere size-parameter are shown in the range of size-parameters 0 ka less than 30.0. The reflection form-functions may be calculated at any distance from the elastic sphere by one of two formulas, one describing reflection in the far-field case. A description is given of the means by which the spherical Bessel function values, required in computations made using the reflection formulas, are calculated. Examples are given of form-function computational results in the case of reflection by elastic spheres and, for purposes of comparison, also in the case of reflection by rigid, immovable spheres. Brief tables of computed values of the far-field reflection form-function as a function of sphere size-parameter are given in the cases of an aluminum and of a rigid sphere. Implementation of the numerical methods described requires access to a digital computer. The capabilities and limitations of the two different computing machines used in the treatment of the elastic sphere problem by the numerical methods described, are discussed. Author