A Mathematical Analysis of a Free-Flooded Finite-Length Radiating Magnetostrictive Shell.

A mathematical analysis with accompanying computer program of the electroacoustic performance of a single finite-length magnetostrictive circular cylinder submerged in an unbounded medium and radiating sound is presented. The cylinder is a thin hyperelastic orthotropic shell constructed of metal laminations and has unrestricted radius to length ratios. Wound toroidally with current carrying coils, it is magnetostrictively excited in axisymmetric modes over selected frequency ranges. In the analysis the vibration of the shell is developed in modes by means of dynamic equations with boundary conditions [Warburton, J. Mech. Eng. Sci. 7, 399 (1965)] and the magnetostriction transduction is described by a set of linearized constitutive relations, also modified to account for hysteresis and eddy currents. New definitions are constructed of modal electromechanical coupling coefficients and modal mass. For an input set of dimensions, electric drive, and selected frequency range, the computer program delivers in vacuo modal frequencies, modal shapes, surface velocities, and electrical and mechanical motional impedances. Typical examples of computer output are given together with a discussion of certain important 'barrel modes.' Comparison is made with selected experimental results. [ABSTRACT FROM AUTHOR]