A note on disturbances in a semi-infinite piezoelectric medium coated with a perfectly conducting thin film

Summary The paper makes use of the constitutive equations of a piezoelectric material and the tool of Laplace transform to investigate the disturbances in a semi-infinite piezoelectric medium coated with a perfectly conducting thin film.     

A note on disturbances in a piezoelectric slab

Summary In the present note, the equations of electricity and the equations of motion have been used to investigate the disturbances in a piezoelectric slab excited by a step electric field. The application of the Laplace transform facilitates the solution of the problem.     

A note on an implementation of a method for quadratic semi-infinite programming

For convex quadratic semi-infinite programming problems aFortran-package is described. A first coarse grid is successively refined in such a way that the solution on the foregoing grids can be used on the one hand as starting points for the subsequent grids and on the other hand to considerably reduce the number of constraints which have to be considered in the subsequent problems. This enables an efficient treatment of large problems with moderate storage requirements. Powell's (1983) numerically stable convex quadratic programming implementation is used to solve the QP-subproblems.     

Transversal line defects induced by an electric field in a period-2 oscillatory medium

The dynamical behavior of spiral waves in a period-2 oscillatory medium is investigated under the influence of an external applied alternating current field. Open and closed transversal line defects which wiggle along the direction parallel to the wave fronts, are generated in the spiral-wave patterns when the stimulus frequency of the electric field is equal to one, three or five times of the local oscillatory frequency in the period-2 state. Their generations are directly related with the change in the spatial wavelength induced by the electric field. These wigglings proliferate along the transverse direction parallel to the wave fronts as the stimulus strength increases, and become denser when the stimulus frequency increases by multiples of the period-2 oscillatory frequency.     

The wave field generated by a centre of rotation in an unbounded elastic medium with a semi-infinite conical crack

The dynamic stress intensity factor at the edge of a semi-infinite conical crack when the medium is loaded by a non-stationary centre of rotation is determined. A centre of rotation is understood to be a set of four forces of equal magnitude that act in the same plane and form pairs having the same direction of rotation.¹ If the magnitude of these forces is time dependent, i.e., their application is non-stationary, they form a non-stationary centre of rotation. The solution of the problem required the use of methods of integral transformations and discontinuous solutions, which reduced the problem to an integral differential equation in Laplace transform space. The combined use of the orthogonal polynomial method and time discretization to solve the equation enabled a formula for the stress intensity factor to be obtained.     

On acoustic and electric waves diffraction in piezoelectric medium by a permeable half-plane crack

The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation” [15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details. The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly. Numerical analysis is presented.     

On acoustic and electric waves diffraction in piezoelectric medium by a permeable half-plane crack

The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation” [15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details. The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly. Numerical analysis is presented.     

Numerical solution of the problem of sound emission by a cylindrical piezoelectric vibrator excited by electric pulses

A numerical method is proposed to solve the nonstationary wave problem for a piezoelectric ceramic cylinder immersed in a liquid and excited by an electric signal. The method uses a finite-difference scheme constructed by the integro-interpolation method. A numerical experiment is conducted to analyze the transients in a thin-walled cylinder excited by a step electric pulse.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 61, pp. 30–37, 1987.     

The deformation of a liquid drop by an electric field

Summary The shape and stability of an incompressible dielectric drop which is stressed by a uniform external electric field are re-examined by considering small perturbations from a prolate spheroid. Compared with the shapes predicted by other approximations it is found that, for a given field strength, the drops should be a little longer and consequently a little flatter at the equator in order to satisfy the equilibrium conditions. It is also shown that beyond a certain drop deformation the L. P. E. (Legendre polynomial expansion) method fails because the equilibrium conditions at the surface of the drop are not satisfied.     

Scattering on an anisotropic potential in a constant electric field

The scattering of a particle on an anisotropic potential in a constant electric field is considered. Conditions on the anisotropic decay of the potential that insure asymptotic completeness without modifications of the wave operators are obtained. The paper uses the mixed approach wherein the Enss method is applied to one part of the variables, whereas the other part is treated using the smoothness technique. Bibliography: 12 titles. Translated fromZapiski Naucnykh Seminarov POMI, Vol. 230, 1995, pp. 203–214. Translated by A. B. Pushnitskii.     

An iterative method for computing the anomalous electric field in a conducting medium

Translated from Metody Matematicheskogo Modelirovaniya i Vychislitel'noi Diagnostiki, pp. 162–171, Izd. Moskovskogo Universiteta, Moscow, 1990.     

On diffraction in a piezoelectric medium by a half-plane: The Sommerfeld problem

This paper is concerned with the diffraction problem in a transversely isotropic piezoelectric medium by a half-plane. The half-plane obstacle considered here is a semi-infinite slit, or a crack; both its surfaces are traction free and electric absorbent screens. In a generalized sense, we are dealing with the Sommerfeld problem in a piezoelectric medium.¶The coupled diffraction fields between acoustic wave and electric wave are excited by both incident acoustic wave as well as incident electric wave; and the sound soft and electric "blackness" conditions on the screens are characterized by a system of simultaneous Wiener-Hopf equations. Closed form solutions are sought by employing special techniques. Some interesting results have been obtained, such as mode conversions between acoustic wave and electric wave, novel diffraction patterns in the scattering fields, and the effect of electroacoustic head wave, as well as of surface wave-Bleustein-Gulyaev wave.¶Unlike the classical Sommerfeld problem, in which the only concern is the scattering field of electric wave, the strength of material, e.g. material toughness, is another concern here. From this perspective, relevant dynamic field intensity factors at the crack tip are derived explicitly.