Showing papers in "Journal of Applied Mathematics and Mechanics in 2013"

TL;DR: In this article, the fundamental theory of accreting bodies for finite deformations is explained using the concept of the bundle of a differentiable manifold that enables one to construct a clear classification of the accretion processes.

TL;DR: An approximate semi-analytical method for solving integral equations generated by mixed problems of the theory of elasticity for inhomogeneous media is developed in this article, where an effective algorithm for constructing approximations of transforms of the kernels of integral equations by analytical expressions of a special type is proposed, and closed analytical solutions are presented.

TL;DR: In this article, the optimal game problem is reduced to an infinite system of differential equations with integral constraints on the players' controls, and the goal of the pursuer is to bring the system into the zeroth state, while the evader strives to prevent this.

TL;DR: In this article, the propagation of sound waves in two-fraction mixtures of a liquid with polydisperse gas bubbles of different composition is investigated, and a system of differential equations of the perturbed motion of the mixture is presented.

TL;DR: In this paper, a solution of the plane problem of the theory of elasticity for a film-substrate composite is solved by a perturbation method for a substrate with a rough surface.

TL;DR: In this article, a closed system of equations in the water level perturbations and the velocity potential is derived to describe them, using the method of multiple scales and perturbation theory, and a periodic solution of the equation obtained is constructed, expressed in terms of Weierstrass elliptic functions.

TL;DR: In this article, the time-optimal problem for a controlled system with evolution-type distributed parameters is considered and an upper estimate is obtained for the optimal transition time into the zero state.

TL;DR: In this article, a solution of the plane problem of the contact interaction of a periodic system of convex punches with an elastic half-plane is given for two forms of boundary conditions: sliding of the punches when there is friction and wear, and indentation of the punched when there are adhesion.

TL;DR: In this article, the development of the single mode flutter of an elastic plate in a supersonic gas flow is investigated in a non-linear formulation, in which a unique limit cycle corresponds to a unique growing mode.

TL;DR: In this paper, the selfbalancing of a statically unbalanced orthotropic elastic rotor equipped with a ball auto-balancing device is investigated, and the conditions for a steady balanced mode of motion for an orthotropic rotor to exist have the same form as for an isotropic rotor.

TL;DR: In this article, the behavior of an oscillatory mechanical system with alternating dissipation is considered taking an aerodynamic pendulum as an example, and phase portraits are investigated, their rearrangements are studied and the critical values of a parameter are determined.

TL;DR: In this article, the principles of the proof of the existence of homoclinic orbits in dissipative dynamical systems are described and applied to the case of a Lorenz system.

TL;DR: In this paper, a refined formulation of the contact problem when there are intermolecular interaction forces between the contacting bodies is considered, where these forces are applied to points within the body, rather than to the surface of the deformable body as a contact pressure, and the body surface is load-free.

TL;DR: An exact solution of the quasistatic problem of elastoplastic theory of the development of the flow of an incompressible medium in a cylindrical tube of circular cross section due to an increase in the pressure drop with time, and on the subsequent flow when there is a constant pressure and a deceleration due to its slow reduction is given in this article.

TL;DR: In this article, the authors extended Rakhmatulin's problem of an unloading wave for a linear strengthening scheme to the case of large values of the maximum pressures, and presented two versions of the solution of this problem as they apply to the non-linear "stress-strain" diagram of elastoplastic materials.

TL;DR: In this paper, the problem of the elastoplastic deformation of reinforced plates taking account of their reduced shear strength is formulated in rectangular Cartesian and cylindrical systems of coordinates within the framework of deformation-type constitutive relations based on the first version of Timoshenko's theory.

TL;DR: In this article, the axisymmetric static problem of the stress-strain state of two hollow circular elastic cylinders, one of which is predeformed and inserted into the other cylinder, is considered in the case of large plane deformations (an extension of the Lame-Gadolin problem to large deformations).

TL;DR: In this paper, a non-linear analysis of the orbital stability of plane periodic motions (pendulum oscillations and rotations) of a dynamically symmetrical heavy rigid body with one fixed point is carried out.

TL;DR: In this paper, the authors introduced the concept of coupled subsystems (MSCCS) and analyzed the entire system, including the oscillations, bifurcation, stability, stabilization and resonance.

TL;DR: Sufficient conditions for simultaneous multiple capture are obtained in a linear non-stationary conflict-controlled process with different dynamic and inertial possibilities of all the participants.

TL;DR: In this paper, simple Riemann waves are investigated within the von Mises elastoplasticity model with hardening, where preceding processes have brought the medium into a state corresponding to a certain point on the loading surface.

TL;DR: In this paper, the existence of limit periodic solutions with resonance, caused by coincidence between the periodic part of the limit external periodic perturbation and the natural frequency of the linearized system, is solved.

TL;DR: A general theorem on the behaviour of the angular variables of integrable dynamical systems as functions of time is established in this article, where problems on the motion of the nodal line of a Kovalevskaya top and of a three-dimensional rigid body in a fluid are considered as examples.

TL;DR: In this paper, a method for the approximate solution of the problem of many bodies of spherical form in a viscous fluid is developed in the Stokes approximation, based on the use of the concept of a self-consistent field.

TL;DR: In this paper, the properties of eigenwaves in laminated plates with anisotropy in a transforse directon properties are studied and the most general form of the solutions, dispersion relations, power flows and generalized orthogonality relations are analyzed.

TL;DR: In this article, the perturbed flow in a laminar boundary layer is investigated when there are heating elements on the body surface, and a solution of a plane steady-state problem is constructed in the linear approximation.

TL;DR: In this paper, a phenomenological method is proposed for calculating the residual stress and plastic deformation fields in a hollow surface-hardened cylindrical sample, and the tensor fields of the residual stresses and deformations are constructed assuming the hypothesis of surface hardening anisotropy and the absence of secondary plastic compression deformations.

TL;DR: In this article, a semi-analytical approach is proposed for constructing an effective solution of the problem of high-frequency diffraction of elastic waves by a crack in an isotropic plane.

TL;DR: In this article, the authors investigated the self-sustaining self-destructive flow around a circular cone under the classical formulation of an infinitely thin detonation wave (DW) in an inviscid and nonheat conducting combustible mixture.

TL;DR: In this paper, a new family of kinematic parameters for the orientation of a rigid body (global and local) is presented and described by mapping the variables onto a corresponding orientated subspace (hyperplane).