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The paper studies the interaction of a spherical shock wave with an elastic circular cylindrical shell immersed in an infinite acoustic medium. The shell is assumed infinitely long. The wave source is quite close to the shell, causing deformation of just a small portion of the shell, which makes it possible to represent the solution by a double Fourier series. The method allows the exact determination of the hydrodynamic forces acting on the shell and analysis of its stress state. Some characteristic features of the stress state are described for different distances to the wave source. Formulas are proposed for establishing the safety conditions of the shell.Consider an infinitely long elastic circular cylindrical shell immersed in an infinite fluid. A point source of shock waves (SWs) is located at a distance R 0 from the shell axis. A spherical SW is diffracted by the shell, and while deforming, the shell generates radiation waves. Therefore, the stress analysis of the shell must involve the simultaneous solution of the equations of motion of the fluid and shell coupled by boundary conditions at the shell surface. Though various approaches were considered in [1-3, 5, 6, 11, 13, 14, etc.] to solve this problem, no exact and complete results have been obtained yet.The findings in nonstationary elasticity and hydroelasticity are discussed in [14,16,18]. We will solve the problem on the basis of linear theory. Let the shell radius r 0 , the density of the fluid ρ 0 , and the sonic velocity in the fluid c 0 be units of measurement. Then all other quantities are measured in terms of fractions of the power complex r c 0 0 0 α β γ ρ that has the same dimension as a given quantity. With such an approach, all dependences will be dimensionless, which is convenient for theoretical analysis. We will describe the deformation of the shell using the linear theory of shells based on the Kirchhoff-Love hypothesis. Let the displacements of the shell's median surface, u, ν, and w, be the basic variables. Then, written in a cylindrical coordinate system x, r, θ whose axis coincides with the shell axis, the equations of motion of the shell take the following form [11]:
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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