Abstract
The problem of sound emission is considered by a system formed from cylindrical piezoceramic radiators with internal acoustically soft screens. Longitudinal axis of emitters lie in one plane. This system is characterized by the interaction of electric, mechanical and acoustic fields in the process of conversion electrical energy to acoustical energy and acoustic fields in the process of forming them in the environments. The purpose of the work is to determine the peculiarities of the electromechanical acoustic transformation of energy by cylindrical piezoceramic radiators with internal screens in the composition of flat systems, taking into account all types of interaction.The research was carried out by the method of bound fields in multiply connected domains with the use of addition theorems for the cylindrical wave functions. The physical fields arising from the emission of sound by such a system are determined by the joint solution of the system of differential equations: the wave equation; equations of motion of thin piezoceramic shells with circular polarization in displacements; the equations of forced electrostatics for piezoceramics at given boundary conditions, the conditions of conjugation of fields at the boundaries of the division of domains and electric conditions.The solution of the problem is reduced to the solution of an infinite system of linear algebraic equations with respect to unknown coefficients of field expansions.An analysis of the results of numerical calculations, performed on the basis of the obtained analytical relations, called to establish a number of features in the electromechanical acoustic transformation of energy by emitters in the composition of flat systems. They include: the role of acoustic interaction in the process of energy conversion; determination of the mechanism of quantitative assessment of the influence of interaction on these processes; the dependence of the degree of violation of the radial symmetry of the acoustic loading of the emitters on the amount of acoustic interaction; the appearance of multimodality of the mechanical field of emitters in the structure of the plane system and the dependence of the redistribution of energy between all modes on the degree of disturbance of the radial symmetry of the acoustic loading of the emitters.
Highlights
An analysis of the results of numerical calculations, performed on the basis of the obtained analytical relations, called to establish a number of features in the electromechanical acoustic transformation of energy by emitters in the composition of flat systems
The problem of sound emission is considered by a system formed from cylindrical piezoceramic radiators
Longitudinal axis of emitters lie in one plane
Summary
Электрически призмы включены параллельно, благодаря чему векторы напряженности электрического поля и механических деформаций параллельны (окружная поляризация). – уравнений движения тонких пьезокерамических оболочек с окружной поляризацией в перемещениях: при нулевой деформации, пьезоконстанта, плотность материала пьезокерамической оболочки s-го излучателя; E и D – векторы напряженности и индукции электрического поля. Φ1( s потенциал скорости полного поs =1 ля излучения рассматриваемой системы; σrs – нормальная составляющая тензора механических напряжений в пьезокерамике s-го излучателя. Электрические условия состоят в задании напряженности электрического поля в пьезокерамической оболочке каждого излучателя (s = 1, ..., N) системы в виде: Eφs. N ( ) ∑ ( ) ( ) Nm ksαs kslOs′Os e N i(m− )n φOs′Os n ks rs einφs , n где rqs, losos и φqs, φοs'os – полярные координаты начала координатной системы Os в координатах систем с началами Oq и O's. Позволяет получить для отыскания неизвестных коэффициентов разложений (9) следующую бесконечную систему линейных алгебраических уравнений:
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