On Singularities of the Physical Fields at the Edge of a Composite Wedge

We propose analytic procedures capable of evaluation of the orders of power singularities of magnetic fields at the edge of a composite ferromagnetic wedge bordering with a vacuum. The same procedure is used to study the singularities at the edge of a composite piezoceramic wedge. As a result, we present the plots characterizing the dependences of the order of singularities on the wedge angles of the wedges used to form the analyzed composite wedge and the combination of their physical parameters.     

Optimal Control over Wave Motions of a Piezoceramic Rod

We solve the direct problem of longitudinal wave motions of a piezoceramic rod under the action of electric excitations variable as a function of time. The solutions obtained as a result explicitly depend on the applied voltage. Interpreting the rate of changes in the electric voltage as a function of control, we pose and solve two problems of optimal control, namely, the problem of transfer of the observed points of the rod into prescribed positions by minimizing the norm of control and the problem of transfer of the rod with the best possible rate and certain restrictions imposed on the norm of control. The results of numerical analysis of the time dependence of the optimal electric voltage applied to the rod are presented and the plot of the norm of optimal control versus the period of control is constructed.     

Homogeneous Solutions of a Skew-Symmetric Problem with Mixed Boundary Conditions for a Piezoceramic Layer

On the basis of a modified scheme of homogeneous solutions significantly simplifying the Lur'e scheme, we construct homogeneous solutions for a piezoceramic layer with mixed boundary conditions imposed on its faces. We consider an electroelastic state skew-symmetric about the median plane of the layer. It is shown that the corresponding homogeneous solutions do not contain biharmonic terms and the components of the conjugate electroelastic field in the layer have the form of Fourier series with respect to the coordinate x ₃.     

Revised Analysis of Homogeneous Solutions for an Elastic Layer

We construct the solution of the homogeneous Lamé equations for a layer with mixed boundary conditions imposed on its surfaces. The analyzed stressed state is skew-symmetric about the middle plane of the layer (x ₃ = 0). It is shown that the homogeneous solutions corresponding to this case do not contain biharmonic components.