The effect of the fluid-filled borehole on operation of a piezoceramic ultrasonic emitter is explored by numerical modeling within the framework of following model. Two identical piezoceramic rods of round cut, disposed coaxially on given distance from each other, are built in adjacent ends of the two absolutely rigid tubes of the same cut. When the variable voltage is applied to ends of the rods, the adjacent ends perform anti-phase oscillations in axial direction. This device is centered in fluid-filled borehole of round cut drilled in a homogeneous elastic medium. It is enough to use the one-dimensional approximation for description of distribution of elastic oscillations in the rod, that allows receiving the desired solution in quadratures at the given mechanical impedance of this emitter. The values of this impedance as function of frequency are determined from numerical solution of the direct problem about acoustic waves distribution in the above-mentioned medium giving the rod end velocity as the temporal function with enough big of spectrum width. The proposed approach allows approximate determining optimum parameters of such emitter in acoustic logging and bed stimulation problems.

Mathematical modelling in actual problems of science and technics