Radiation of Sound by a Cylindrical Piezoceramic Converter with Radial Polarization and a Rigid Screen

Abstract

In this paper, the acoustic antenna was disassembled, the reflector of which was made in the form of an acoustically rigid screen, and the sound source is a cylindrical piezoceramic converter with radial polarization. The height of the radiator is infinitely large, so the velocity distribution is uniform. The internal volume of the converter is filled with vacuum or gas, and radial polarization is realized by applying the electrodes on the cylindrical surfaces of the shell. The electrodes of the shell are brought into harmoniously changing time electric voltages and frequencies. The thickness of the rings of the cylindrical converter is taken much less than the average radius. We believe that the height of the emitter is infinitely large, so the distribution of the oscillation velocity along the height of the emitter is homogeneous. Analytical relations were described that describe the acoustic fields of cylindrical piezoceramic converters with rigid acoustic screens in the form of unclosed annular torus. The problem of the radiation of sound with such an antenna was solved using the methods of bound fields and partial regions. All physical antenna fields are represented in the form of decompositions in Fourier series, the coefficients of which are determined as a result of the solution of differential equations describing the electroshock oscillations of the piezoceramic converter and the wave processes in acoustic media in contact with it. The boundary conditions are formulated for the inner and outer walls of the screen, and also the electric field strength in the shell material, which describes the operation of the screened converter, is taken into account. That is, on the surface of the converter in contact with the medium, the equation of the normal displacement of the surface of the piezoceramic shell and the oscillatory velocity of the particles of the medium, both external - working and internal, located inside the converter, is formed. The complete system of output ratios of the task includes the conditions for conjugation of sound fields at the boundaries of the division of regions and boundary conditions on the outer surface of the screen. According to the boundary conditions, the potential of the acoustic field velocity created by the converter was presented, because of the velocity potential in each of these regions. The solution of the problem of sound radiation is reduced to the solution by the reduction method of an infinite system of linear algebraic equations. The paper presents the analytical relations of sound pressure on the surface of the emitter shell, depending on the frequency and angle of the opening, as well as the expression for determining the characteristics of the direction of cylindrical piezoceramic converters with rigid acoustic screens.