Moscow University Mechanics Bulletin最新文献

The paper considers the problem of unsteady wave propagation in the cross section of an infinite hollow cylinder made of a viscoelastic functionally graded material with nonmonotonically varying properties along the radius. The cylinder is replaced by a piecewise-homogeneous one with a large number of coaxial homogeneous layers approximating the properties of the source material. Based on the previously constructed solution for a layered cylinder, wave processes in a cylinder made of a viscoelastic functionally graded material with different types of nonmonotonic inhomogeneities are studied.

The problem is considered for the indentation of a functionally graded strip by a rigid punch of finite dimension with a surface microrelief. Boundary variational formulations of the problem are given using the Poincaré–Steklov operator that maps contact stresses to displacements. To approximate this operator, the discrete Fourier transform is applied. A variational formulation of a boundary value problem for transforms of displacements is used to calculate a transfer function. Some regularities of contact interaction are established.

This paper uses the assumption on the smallness of deformations, flexural-torsional characteristics and angles of rotation of the shell elements, as well as the assumption on shell’s shallowness. Based on this assumption, a geometrically nonlinear moment-membrane theory of elastic shells is constructed with the help of the three-dimensional geometrically nonlinear moment theory of elasticity and by preserving only those nonlinear terms that come from normal displacement (deflection) and its derivatives. The constructed theory is interpreted as a continuum theory of the deformation behavior of flexible two-dimensional nanomaterials, in particular, of carbon nanotubes and graphene.

We investigate three-phase flows in porous media caused by carbon dioxide and water injection into an oil reservoir. We construct a numerical model of the flow complicated by the phase transitions between oil and gas and the hysteresis changes in the gas relative permeability. The model is coupled with the economic estimates of the profitability of oil recovery. Using a numerical model, we estimate the effect of the hysteresis on the most profitable strategies of the alternating injection of water and carbon dioxide. We show that the hysteresis behavior requires the injection of larger volumes of gas to maximize the profit.

In the paper we continue the research on the modified Hodgkin–Huxley model in the presence of random noise. It is shown that, adding a certain short-time stimulation current, a random noise of low amplitude does not prevent the system transition from the motion within a neighborhood of the small stable limit cycle (the mode ‘‘None’’ in accordance with the principal neurophysiological ‘‘All or none’’-law) to the motion along the big stable limit cycle called ‘‘duck nose’’ (the mode ‘‘All’’ respectively). At the same time, the high amplitude random noise can yield a series of transitions from one regime to the other and vice versa, even for a short-time stimulation. In the absence of stimulation and in the presence of high amplitude noise, such series of transitions were observed earlier during computer simulation.

From the standpoint of the theory of small elastoplasticdeformations, the stress-strain state of the continuous mediumalong various unloading trajectories from the state achieved as aresult of a simple active process is analyzed. It is shown that ifthe unloading is disproportionate, then the constitutive relationsconnecting the deviators of stresses and strains are tensoriallynonlinear, i.e., the unit tensors of these deviators do notcoincide. It is demonstrated that in the Il’yushinfive-dimensional deviatoric space there exists only one fullunloading point, and it belongs to the line segment of thepreceding active loading. A measure of the nonproportionality ofthe unloading is introduced, characterizing the degree ofdeviation of the path of the passive deformation process from thepreviously mentioned line segment. This measure is calculated fortwo piece-linear unloadings using the example of a constantannular tube subject to the simultaneous action of ((rtheta))-torsion and axial ((rz))-shear.

In this paper, a variational principle of Lagrange, the Ritz method, and piecewise polynomial shape functions of brick family ‘‘linear’’ element are used to obtain reduced and selective integration techniques in a form of the tensor-block stiffness matrices to prevent the locking effect for nearly incompressible, isotropic, and centrally symmetric material of the micropolar theory of elasticity.

This paper shows the possibility of solving the problem of the transition between periodic and point attractors in the bistable Rosenzweig–MacArthur model with modifications for the dynamics of root hemiparasitic plants and their hosts.

The article presents a three-dimensional linear model of the vestibulo-ocular reflex in darkness. The model is based on established relationships between the vestibular system and the extraocular muscles. The effectiveness of the model is evaluated through comparison with experimental observations. The model successfully reproduces realistic patterns of slow-phase vestibulo-ocular nystagmus during head rotations.

An exact analytic solution to the problem of joint nonstationary oscillations of a semi-infinite underground pipeline and elastic soil caused by the propagation of a longitudinal seismic wave along its axis is obtained in the case when the pipeline end is clamped. The emerging stress-strain state for subsonic and supersonic modes of seismic wave propagation is studied. The results of this study can be used to calculate the deformation of oil and gas pipelines under seismic loads.