The paper describes analytical approach solving the problem of dynamic analysis of two-dimensional fields of vibrational displacements and rotations caused by magnetic forces acting on stator of AC machine. Final set of three differential equations converted into algebraic ones is given and it is confronted with numerical solutions obtained by finite element method.
This paper presents a method of calculation of steady-state processes in threephases matrix-reactance frequency converters (MRFC's), in which voltages and currents are transformed by control signals with two pulsations. A solution of nonstationary differentia equations with periodic coefficients that describe this system is obtained by using Galerkin's method and an extension of equations of one variable of time to equations of two variables of time. The results of calculations are presented in an example of three-phases MRFC with buck-boost topology and compared with a numerical metod embedded in the program Mathematica.
This work presents a study on dynamics of a circuit with a non-linear coil, where loss in iron is also taken into account. A coil model is derived using a state space description. The work also includes the development of an application in C# for coil dynamics examination, where the implicit RADAU IIA method of various orders is applied for the purpose of solving non-linear differential equations modelling the non-linear coil with loss in iron.
Although the explicit commutativitiy conditions for second-order linear time-varying systems have been appeared in some literature, these are all for initially relaxed systems. This paper presents explicit necessary and sufficient commutativity conditions for commutativity of second-order linear time-varying systems with non-zero initial conditions. It has appeared interesting that the second requirement for the commutativity of non-relaxed systems plays an important role on the commutativity conditions when non-zero initial conditions exist. Another highlight is that the commutativity of switched systems is considered and spoiling of commutativity at the switching instants is illustrated for the first time. The simulation results support the theory developed in the paper.
The purpose of this work is to present a theoretical analysis of top orthogonal to bottom arrays of conducting electrodes of infinitesimal thickness (conducting strips) residing on the opposite surfaces of piezoelectric slab. The components of electric field are expanded into double periodic Bloch series with corresponding amplitudes represented by Legendre polynomials, in the proposed semi-analytical model of the considered two-dimensional (2D) array of strips. The boundary and edge conditions are satisfied directly by field representation, as a result. The method results in a small system of linear equations for unknown expansion coefficients to be solved numerically. A simple numerical example is given to illustrate the method. Also a test transducer was designed and a pilot experiment was carried out to illustrate the acoustic-wave generating capabilities of the proposed arrangement of top orthogonal to bottom arrays of conducting strips.
This paper presents the concept of using algorithms for reducing the dimensions of finite-difference equations of two-dimensional (2D) problems, for second-order partial differential equations. Solutions are predicted as two-variable functions over the rectangular domain, which are periodic with respect to each variable and which repeat outside the domain. Novel finite-difference operators, of both the first and second orders, are developed for such functions. These operators relate the value of derivatives at each point to the values of the function at all points distributed uniformly over the function domain. A specific feature of the novel operators follows from the arrangement of the function values as well as the values of derivatives, which are rectangular matrices instead of vectors. This significantly reduces the dimensions of the finite-difference operators to the numbers of points in each direction of the 2D area. The finite-difference equations are created exemplary elliptic equations. An original iterative algorithm is proposed for reducing the process of solving finite-difference equations to the multiplication of matrices.