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Abstract:
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New mathematical methods to analytically investigate linear acoustic radiation
and scattering from cylindrical bodies and transducer arrays are presented. Three
problems of interest involving cylinders in an infinite fluid are studied. In all the three
problems, the Helmholtz equation is used to model propagation through the fluid and the
beam patterns of arrays of transducers are studied.
In the first problem, a method is presented to determine the omni-directional and
directional far-field pressures radiated by a cylindrical transducer array in an infinite
rigid cylindrical baffle. The solution to the Helmholtz equation and the displacement
continuity condition at the interface between the array and the surrounding water are
used to determine the pressure. The displacement of the surface of each transducer is in
the direction of the normal to the array and is assumed to be uniform. Expressions are
derived for the pressure radiated by a sector of the array vibrating in-phase, the entire
array vibrating in-phase, and a sector of the array phase-shaded to simulate radiation
from a rectangular piston. It is shown that the uniform displacement required for
generating a source level of 220 dB ref. μPa @ 1m that is omni directional in the
azimuthal plane is in the order of 1 micron for typical arrays. Numerical results are
presented to show that there is only a small difference between the on-axis pressures
radiated by phased cylindrical arrays and planar arrays. The problem is of interest
because cylindrical arrays of projectors are often used to search for underwater objects.
In the second problem, the errors, when using data-independent, classical, energy
and split beam correlation methods, in finding the direction of arrival (DOA) of a plane
acoustic wave, caused by the presence of a solid circular elastic cylindrical stiffener near
a linear array of hydrophones, are investigated. Scattering from the effectively infinite
cylinder is modeled using the exact axisymmetric equations of motion and the total
pressures at the hydrophone locations are computed. The effect of the radius of the
cylinder, a, the distance between the cylinder and the array, b, the number of
hydrophones in the array, 2H, and the angle of incidence of the wave, α, on the error in
finding the DOA are illustrated using numerical results. For an array that is about 30
times the wavelength and for small angles of incidence (α<10), the error in finding the
DOA using the energy method is less than that using the split beam correlation method
with beam steered to α; and in some cases, the error increases when b increases; and the errors in finding the DOA using the energy method and the split beam correlation
method with beam steered to α vary approximately as a7 / 4 . The problem is of interest
because elastic stiffeners – in nearly acoustically transparent sonar domes that are used to
protect arrays of transducers – scatter waves that are incident on it and cause an error in
the estimated direction of arrival of the wave.
In the third problem, a high-frequency ray-acoustics method is presented and
used to determine the interior pressure field when a plane wave is normally incident on a
fluid cylinder embedded in another infinite fluid. The pressure field is determined by
using geometrical and physical acoustics. The interior pressure is expressed as the sum
of the pressures due to all rays that pass through a point. Numerical results are presented
for ka = 20 to 100 where k is the acoustic wavenumber of the exterior fluid and a is the
radius of the cylinder. The results are in good agreement with those obtained using field
theory. The directional responses, to the plane wave, of sectors of a circular array of
uniformly distributed hydrophones in the embedded cylinder are then computed. The
sectors are used to simulate linear arrays with uniformly distributed normals by using
delays. The directional responses are compared with the output from an array in an
infinite homogenous fluid. These outputs are of interest as they are used to determine the
direction of arrival of the plane wave. Numerical results are presented for a circular array
with 32 hydrophones and 12 hydrophones in each sector. The problem is of interest
because arrays of hydrophones are housed inside sonar domes and acoustic plane waves
from distant sources are scattered by the dome filled with fresh water and cause
deterioration in the performance of the array. |