MUTUAL AND SELF-RADIATION IMPEDANCES IN AN ARRAY OF FREE-FLOODING, COAXIAL, SPACED RING TRANSDUCERS
Abstract
Expressions are derived for the mutual and self radiation impedances between the elements in an array of coaxial, free-flooding, axially spaced ring transducers undergoing axisymmetric, radial vibrations. Fluid circulation through the gaps between elements and around the array extremities is accounted for in a formulation of this problem which was presented in a recent study of single ''squirters.'' An integral equation is constructed which defines the unknown radial velocity distribution alpha(z) between elements and on the two semi-infinite cylindrical surfaces which bracket the array. It is shown that the radiation impedance is the sum of two components: (1) the impedance evaluated by means of the mathematical model originated by Robey, which assumes that the active array element is located on an infinite rigid cylindrical baffle, and (2) the impedance associated with the unknown velocity distribution alpha(z), which is therefore in the nature of a correction factor to Robey's impedance. Four methods are presented for obtaining the function alpha(z): a perturbation solution which can be used as the starting point in a more refined iteration- type solution, a finite difference solution of the integral equation and finally a variational solution.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1964
- Accession Number
- AD0434698
Entities
People
- Miguel C. Junger