Electroacoustic Modeling of Magnetostrictive Shells and Rings: Part 1. Mathematical Modeling.
NAVAL RESEARCH LAB WASHINGTON D C
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The basic canonical equations of a matrix of n linear coupled electroacoustic transducers are stated in matrix form from them are derived by matrix inversion the electroacoustic parameters of performance n-port voltages, currents, velocities, forces with associated electrical and mechanical impedances. The problem of the mechanical vibration of a thin magnetostrictive shell is formulated in abstract operator form, then specialized to the case of a finite-length, axisymmetric, free-flooded magnetostrictive shell. Acoustic loading is accounted for by converting the differential equations of motion into a set of linear integral equations in unknown surface velocities, which are solved by inversion of a set of equivalent algebraic equations. The concepts of electromechanical modal mass and modal coupling are introduced in three alternative formulations. Details on the method of calculating the acoustic loading of a finite-length, axisymmetric, free-flooded magnetostrictive shell are then presented. In an appendix is a digest of the mathematical model of a free-flooded magnetostrictive shell of very short axial length, that is, a ring.
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