Generation of nonstationary waves by a thick-walled piezoceramic cylinder excited by electric signals

Abstract

Coupled electroelasticity theory, acoustic approximation, and two-wire transmission line theory are used to study the generation of waves by a submerged cylindrical piezoelectric transducer connected by a cable to a source of nonstationary electric signals. The problem is reduced to a system of integral Volterra equations using the Laplace transform and analytical inversion of boundary conditions. The results of calculations for different cable lengths are presented Keywords: electroelasticity, piezoelectricity, generation of nonstationary waves, two-wire line Most studies on electroelasticity and hydroelectroelasticity have been carried out for time-periodic dynamic processes [5,8]. The significance of these results does not detract from the importance of such problems in a nonstationary formulation. This is due to the wide application of piezoceramic transducers that operate in pulse modes. There was a series of studies in which such problems were formulated assuming a potential difference between conductive coatings of the transducer. In addition to periodic publications (such as [12,13]), these results are partially generalized in the monograph [1] and review [14]. Of the recent studies on nonstationary continuum mechanics, it is worthwhile to mention the papers [9,16,17]. There are hydroelectroelastic systems where the piezoelectric transducer and the generator are spaced far apart and connected by a long cable. The influence of such a wire line on the transient characteristics was analyzed in [10,11,15], where the transducer is thin-walled and its behavior is described by the theory of electroelastic shells based on the Kirchhoff-Love hypotheses [5].The present paper addresses the problem of wave generation by a thick-walled, infinitely long, cylindrical piezoelectric transducer immersed in a perfect compressible liquid. The solid conductive coatings on the inner and outer surfaces of the transducer are connected by a two-wire line with distributed parameters (cable) to a source of nonstationary electric signals. The medium inside the cylinder is vacuum. A similar problem where a transducer is excited by a signal supplied directly to its electrodes was solved in [2].The dynamic processes in the hydroelectroelastic system in question are modeled using coupled electroelasticity theory [5], acoustic approximation, and two-wire transmission line theory [3].We will use the following notation: u r is the radial displacement of the transducer; σ rr and σ θθ are the radial and circumferential components of the stress tensor; Ψ and D r are the potential and electric displacements of the electric field; C E 11 , C E 13 , and C E 33 are the elastic moduli; ρ c is density; e 33 and e 31 are the piezoelectric moduli; d 33 is a piezoelectric constant; ε 33 s is the dielectric permittivity of the material; R 1 and R 2 are the outer and inner radii of the cylinder; r is the radial coordinate; ϕ is the velocity potential of the ambient acoustic medium; p and V r are the pressure and velocity in this medium; ρ and c are its ...

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