Moscow University Mechanics Bulletin最新文献

Possible statements of mathematical problems arising from topics in special courses in mechanics are discussed.

The nonstationary dynamic viscoelasticity problem for a piecewise homogeneous body is considered. It is known that, under certain conditions, the construction of a solution to such a problem can be reduced to finding the eigenvalues of the free oscillation problem. The properties of a spectral set are considered, and a method for searching for its elements if proposed. The theoretical considerations are used to study the unsteady dynamics of a piecewise homogeneous viscoelastic plane-parallel layer. For some specific parameters of this layer, the elements of the spectrum are found, and, then, the transition wave process is studied.

A conservative system with one degree of freedom admitting a periodic motion is considered. The system is located on a translationally moving base. Linear viscous friction forces are added to the forces acting on the points of the system. We determine the law of motion of the base that allows preserving the periodic motion of the initial system relative to this base. The conditions when the periodic motion becomes Lyapunov asymptotically stable are obtained by using the Vazhevsky inequality.

Various hypotheses proposed with the Il’yushin plasticity theory framework and expressed in terms of ODEs and multiple integrals are studied. One of the key aspects of this approach is a classification of constitutive equations by the complexity of loading for which a certain relation is suitable. Some relations of markedly different forms are proposed for a group of strain paths with moderate curvatures; this group is the most general kind of stress-strain relations in this classification. In the present paper the connections between those relations are discussed.

A review of the works devoted to the theoretical study and experimental verification of one of the fundamental hypotheses of the theory of processes by A.A. Il’yushin, the particular postulate of isotropy, as well as the possibility of its generalization to initially anisotropic materials is fulfilled. A formulation of such a generalization is proposed using the concept of invariant subspaces of the symmetry group of an anisotropic material. As an example, within the framework of the proposed generalization, nonlinear constitutive relations for an elastic orthotropic material are constructed.

The paper presents the current results of experimental studies of the creep properties of metallic materials and related processes. Uniaxial tension, the effect of aging and temperature on the strength of a welded joint, complex stress, and the effect of factors of chemical interaction of the environment on creep and creep rupture strength are considered. An equivalent stress is given that allows describing the difference in creep lifetimes under uniaxial tension and under equal multiaxial tension for the same value of the principal stress.

The known physical and phenomenological approaches and failure criteria for structural materials at long-term and variable loading are systematized and their classification are proposed. The modern state of the durability problem is associated with the formulation of multilevel probabilistic models at complex loading, based on the physical laws of processes of brittle and viscous failure.

Wind power generators of oscillatory type use the energy of flow induced vibrations of bodies to generate electricity. Numerous scientific publications are dedicated to development and analysis of various schemes and designs of such devices. The present paper contains a brief review of the literature on this issue.

The article is devoted to the review of scientific achievements of the staff of the Chair of Applied Mechanics and Control, the Laboratories of Control and Navigation and Mathematical Support of Simulation Dynamic Systems in the 21st century.

The presented review consists of two parts. The first one is devoted to research generalizing the classical Prandtl problem in the case of taking into account the inertia of the convergence of rigid plates and dynamic effects occurring in a thin perfect rigid plastic layer. The second part examines the work related to the formation and development of the neck in plastic materials under quasi-static and dynamic loading. In particular, attention is paid to thin solids with a perturbed boundary shape, which have technological significance. The presence of a small geometric parameter allows using the asymptotic methods.