arXiv subjects

Nadezhda Aleksandrova

Publications and source records attributed to Nadezhda Aleksandrova.

10 recordsLinked to original sources

arXiv2018

Pendulum waves on the surface of block rock mass under dynamic impact

Under numerical investigation is propagation of surface pendulum waves in 3D block medium. The medium is modeled by 3D lattice of masses connected with elastic springs and viscous dampers. The surface vertical pulsed concentrated loading is considered. The displacements and velocities of the surface masses are calculated. The numerical results obtained for the block medium are compared with the similar data on elastic medium and in situ experiments carried out by other researchers.

physics.class-ph↗

arXiv2018

Propagation of pendulum waves under deep-seated cord charge blasting in blocky rock mass

The object of the numerical study is the travel of pendulum waves in a blocky medium under nonstationary impact of deep-seated charge blasting on the surface of the expansion chamber. The blocky model is simulated by a two-dimensional lattice of masses connected by elastic springs along the axes and diagonals. The displacements and velocities of the masses at different half-space points are calculated using the finite-difference method.

physics.geo-ph↗

arXiv2018

Influence of soil plug on pipe ramming process

Different modes of advance of a pipe with a soil plug under rectangular impulse are investigated numerically and analytically with regard to dry friction between the pipe and plug and between the pipe and external stationary medium. The two model solutions are compared with and without regard to the pipe and plug elasticity. It is shown that elasticity of the pipe and plug is neglectable in case of a long-duration impulse.

physics.class-ph↗

arXiv2016

Seismic waves in a three-dimensional block medium

We study numerically the propagation of seismic waves in a three-dimensional block medium. The medium is modeled by a spatial lattice of masses connected by elastic springs and viscous dampers. We study Lamb's problem under a surface point vertical load. The cases of both step and pulse load are considered. The displacements and velocities are calculated for surface masses. The influence of the viscosity of the dampers on the attenuation of perturbations is studied. We compare our numerical results for the block medium with known analytical solutions for the elastic medium.

physics.class-ph↗

arXiv2014

Asymptotic formulae for the Lommel and Bessel functions and their derivatives

We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. Using the same method we obtain previously known approximate representations of the Nicholson type for Bessel functions and their first derivatives. We study also for what values of the parameters our representations have reasonable accuracy.

math.CA↗

arXiv2014

Deformations of one-dimensional block media

The paper gives a description of wave propagation in discrete-periodic one-dimensional media with block structure. For one-dimensional problems mathematical models are proposed that describe block structures in the form of a mass chain or bars connected by elastic springs and viscous dampers. For these models, the numerical calculations of the parameters of perturbations are obtained as well as asymptotic solutions at large time since the beginning of pulse action. The numerical calculations and analytical solutions are compared.

physics.class-ph↗

arXiv2014

Asymptotic solution of the anti-plane problem for a two-dimensional lattice

Propagation of unsteady waves under the effect of a step point load on a square lattice of spring-connected masses is investigated. The problem is solved by two methods. Asymptotic solutions at large time intervals, which describe the behavior of long-wave perturbations, are derived analytically. The solution over the whole time interval for the waves of the entire spectral range is derived by the finite difference method. These solutions are compared, and their good agreement is shown.

math.AP↗

arXiv2014

The discrete Lamb problem: Elastic lattice waves in a block medium

We study the propagation of transient waves under the action of a vertical step point load on the surface of a half-space filled by a block medium. The block medium is modeled by a square lattice of masses connected by springs in the directions of the axes x, y, and in the diagonal directions. The problem is solved by two methods. Analytically, we obtain asymptotic solutions in the vicinity of the Rayleigh wave at large time intervals. Numerically, we obtain a solution for any finite time interval. We compare these solutions with each other and with the solution to the Lamb problem for an elastic medium.

physics.class-ph↗

arXiv2013

Numerical-analytical investigation into impact pipe driving in soil with dry friction. Part I: Nondeformable external medium

The study focuses on propagation of longitudinal waves in an elastic pipe partly embedded in a medium with dry friction. Mathematical formulation of the problem on the impact pipe driving into the soil is based on the model of longitudinal vibration of an elastic rod with taking into account lateral resistance. The lateral resistance of soil is described by the law of the contact dry friction. Numerical and analytical solutions to problems on longitudinal impulse loading of a pipe are compared.

math.AP↗

arXiv2013

Numerical-analytical investigation into impact pipe driving in soil with dry friction. Part II: Deformable external medium

Under analysis is travel of P-waves in an elastic pipe partly embedded in soil with dry friction. The mathematical formulation of the problem on impact pipe driving in soil is based on the model of axial vibration of an elastic bar, considering lateral resistance described using the law of solid dry friction. The author solves problems on axial load on pipe in interaction with external elastic medium, and compares the analytical and numerical results obtained with and without accounting for the external medium deformability.

math.AP↗