Vol 74, No 5 (2019)

The splitting of initial boundary value problems in the theories of elasticity is considered for some anisotropic media. In particular, the initial boundary value problems of the micropolar classical theory of elasticity are represented using the tensor-block matrix operators (or tensor operators). In the case of isotropic micropolar elastic media known also as isotropic or transversally isotropic classical media, we propose the tensor-block matrix operators of algebraic cofactors corresponding to the tensor-block matrix operators of the initial boundary value problems, which allows us to split these problems.

The motion of a puck on a horizontal plane rotating about a vertical axis with dry friction is considered. It is assumed that the Coulomb law of dry friction is locally valid at each point belonging to the lower surface of the puck. The resultant force and friction torque are determined according to the dynamically consistent model of contact stresses. This problem generalizes the problem of motion of a puck on a fixed plane and the motion of a disk (a puck of zero height) on a rotating plane. The invariant sets of the problem are found and their properties are studied. In the case of a sufficiently small Coulomb friction coefficient, the general solution to the equations of motion of the puck is constructed as a power series expansion with respect to this coefficient.

The dynamic behavior of Bernoulli-Euler and Timoshenko beams subjected to a moving concentrated load is considered. Deflection expressions are found in the form of convergent series for a pretensioned beam and for a beam on an elastic foundation. We determine the parameter ranges for which the results of these two models are coincident. It is shown that, under certain conditions, a resonance is possible in such a system.

The accuracy of stabilization algorithms for a linear system is estimated using maximin testing methods on a finite time interval in the presence of initial and time-varying perturbations.