Use of the pass-through method to solve sound radiation problems of a spherical electro-elastic source of zero order

Abstract

In the article was solved the problem of radiation of a sound by the electroacoustic transducer which is executed in the form of a thin spherical cover, using a pass-through method. The outer and inner surfaces of the shell are completely electroded.
 The application of this method provides an opportunity to avoid inaccuracies that arise during the traditional formulation of boundary conditions for acoustic mechanical fields, the use of equivalent substitution schemes and the absence of boundary conditions for the electric field in general. Given methodology eliminates these shortcomings by applying conjugation conditions, taking into account the types of electroding of the surfaces of piezoceramic transducers, the introduction of boundary conditions for current and voltage. The results of the solution demonstrate the high capabilities of this pass-through method, in terms of taking into account the peculiarities of determining the characteristics of these fields, values and dependences of the main complex characteristics of the electroelastic transducer, and auxiliary material constants of the piezoelectric material.
 The proposed approach is relevant, because it allows to increase the reliability of modeling the operating conditions of acoustic transducers in the context of wave problems of acoustics. Aim is to enhance the range of performances and build algorithms solving problems of stationary mode hydroelectroelasticity sound radiation. The expected results are presented in terms of improving approaches to studying the features of the oscillatory process of the active elements of sound-emitting systems and the accompanying effects of the transformation of interconnected fields involved in the formation of the acoustic signal in the liquid

Mode-Matching Method Applied to the Sound Reception Problem Using Helmholtz Resonator

“…As can be seen, when approaching from the cavity to the angular point, the velocity is twice less than that when approaching from the left along the acoustically 01035-5 rigid boundary to the angular point. This result is confirmed by [6]. That is, at the intersection x  0, the velocity around the corner point can be given by some addition to the regular function vreg and written as…”

“…, n = 0, 1,2, 3, ... (6) Let us turn to area II, which is a closed volume with acoustically rigid walls (boundary condition for the system of functional equations ( 3)). We will assume that the sound field in area II is formed only due to fluctuations in the original cross section of the neck x  0 and repeated reflection of sound waves mainly from the bottom of the cavity x  l2.…”

“…Thus [6], on the boundary   0, series (17) is a complete Fourier series and the conjugation conditions with areas I and II (i.e., for points belonging to space  ≥ 0) should be performed for area III when approaching the angular point from the left (neck) and right (resonator) side. Similar ideas lead to the situation of the acoustic field representation in terms of pressure.…”

“…In this case, the change in velocity at the boundaries of mode-matching areas should be determined by two directions of angular point approach i.e., from area I and from area II. This situation, according to [6], when n  1 determines the velocity at the boundaries with areas I and II, the amplitude of which is obtained after taking the derivatives (18) and substituting the resulting value of the angle…”

“…The method was researched and implemented in acoustic practice by sci-entific schools of the Institute of Hydromechanics of the National Academy of Sciences of Ukraine and the Department of Acoustic and Multimedia Electronic Systems of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute". The main provisions for its application are introduced in [4][5][6][7].…”