The article presents a developed mathematical model of electric describing the coaxial electrogenerating elements (EGE) with isothermal cathode and a variety of ways for current collecting. To analyze their internal state and output parameters in the arc mode we used a two-parameter local linear current-voltage characteristic (CVC). It was shown that in the case of one-sided current collection maximum power of EGE and generated magnetic field asymptotically approach to their maximum values as the length of the electrodes goes into infinity. In the case of versatile current collection maximum values of these parameters can be achieved at the final length of the electrodes. In both methods of the current collection the acceptable value of EGE electrical power loss of 25% due to electrode non-equipotentionality was achieved at their universal critical length. The calculation of which is presented.
Loshkarev A., Oblakova T. Mathematical modeling of coaxial electrogenerating elements. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 3-16
The study deals with the plane stationary problem of elasticity theory on the motion of a vertical concentrated load along the surface of an elastic half-space with a thin coating. The authors investigated modes in the surface layer at speeds close to the resonant speed of the surface wave. The research was done within the long-wave asymptotic model for the Rayleigh wave in the case of an elastic coated half-space. The modes are classified according to the ratio between the velocity of the load and the resonance speed and to the dispersion coefficient of linear coverage. The study discovers the modes having radiation from the source. The results obtained can be generalized to more complex physical properties of the coating material, including the effects of anisotropy, viscosity and prestraining.
Kaplunov J., Oblakova T., Prikazchikov D. Near-resonant modes of the moving load in the plane problem of elasticity theory for a half-space with a thin coating. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 57-67