Radiation of nonstationary acoustic waves by a radially polarized, cylindrical piezoelectric transducer

Numerical solution to the initial-boundary-value problem of electroelasticity for a radially polarized hollow piezoceramic cylinder

“…Two-dimensional nonstationary problems of electroelasticity were solved in [6,9]. The nonstationary electroelastic acoustic vibrations of piezoceramic shells and cylinders in hydraulic systems were studied in [1,2,13].…”

Generation of nonstationary waves by a thick-walled piezoceramic cylinder excited by 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 density and sonic velocity; U and I are the voltage and current in the cable; L * and C * are its capacitance and inductance per unit length; l is the length; x is the Cartesian coordinate running along the cable and reckoned from its input terminals; and t is time.According to the mathematical model adopted, the disturbed state of the piezoceramic cylinder is described by the following system of equations: …”

“…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].…”