24 Result(s)
within
Vladimir I. Erofeev
-
Chapter
Correction to: Structural Modeling of Metamaterials
■■■
-
Chapter and Conference Paper
Influence of Material Damage on the Parameters of a Nonlinear Flexible Wave Which Spread in a Beam
In this paper, a mathematical model is formulated (in linear and nonlinear formulations) and investigated, which makes it possible to describe the propagation of flexural waves in a beam taking into account th...
-
Chapter
Excitation of the Waves with a Focused Source, Moving Along the Border of Gradient-Elastic Half-Space
In the frames of the mathematical model of the gradient-elastic continuum, i.e., the medium with the stress–strain state described by the strain tensor, the second gradients of the displacement vector, the asy...
-
Chapter
Theoretical Basis of the Structural Modeling Method
The principles of the structural modeling method, the development of the theoretical foundations of which this monograph is devoted, are formulated in the first chapter. Moreover, the problem of the applicabil...
-
Chapter
A Two-Dimensional Lattice with Non-dense Packing of Particles
In this chapter, we consider a model of a granular medium as a rectangular lattice of rigid ellipse-shaped particles. Each particle of such a lattice possesses two translational and one rotational degrees of f...
-
Chapter
Nonlinear Models of Microstructured Media
In Chaps. 2–4, the linear models of microstructured media have been considered, the particles of which have three degrees of f...
-
Chapter
Propagation and Interaction of Nonlinear Waves in Generalized Continua
The main goal of the final chapter of the monograph is to study the features of the propagation of nonlinear elastic waves in metamaterials and constructions made of them.
-
Chapter
Linear and Nonlinear Problems of Wave Resistance to the Movement of Objects Along Elastic Guides
The work is devoted to the study of wave resistance to the movement of the load along a flexible guide lying on a linearly elastic foundation or on a nonlinearly elastic foundation. In the case of a rigid type...
-
Chapter
A 2D Lattice with Dense Packing of the Particles
Mechanical properties of a granular consolidated medium depend on the geometry of the microparticles, their location, and the forces of interaction between them. One of the main goals of mathematical modeling ...
-
Chapter
Application of the 2D Models of Media with Dense and Non-dense Packing of the Particles for Solving the Parametric Identification Problems
Theoretical estimates [1] and experimental data [2–5] show that rotational waves can exist in solids in the high-frequency field (> 109 – 1011 Hz), where it is rather difficult to carry out acoustic experiments w...
-
Chapter
A Cubic Lattice of Spherical Particles
In the previous chapters, two-dimensional models of microstructured media were discussed, and the particles of which have three degrees of freedom. This chapter is devoted to the elaboration of a three-dimensi...
-
Chapter
Dispersion, Attenuation and Spatial Localization of Thermoelastic Waves in a Medium with Point Defects
This paper deals with the study of the propagation of plane longitudinal waves in an unbounded point-defected medium located in a nonstationary inhomogeneous temperature field. The problem is considered in the...
-
Chapter
Modulation Instability of Flexural Waves in Cylindrical Shells: Modified Criterion
On the basis of asymptotic analysis of the Kirchhoff-Love cylindrical shell’s element motion equations in displacements a nonintegrable fourth-order quasi-hyperbolic equation with cubic nonlinearity is derived...
-
Chapter
Nonlinear Localized Waves of Deformation in the Class of Metamaterials as Set as the Mass-in-mass Chain
A well-known mathematical model representing a chain of oscillators consisting of elastic elements and masses, each containing an internal oscillator and describing the class of acoustic metamaterials “mass-in...
-
Chapter
Splitting of Strain Solitons upon Their Interaction in the Auxetic Rod
The problem of longitudinal wave propagation in a rod made from an auxetic material is considered. It is shown that a negative Poisson’s ratio leads to a qualitatively different (anomalous) dispersion behavior...
-
Chapter
Structural Modeling of Nonlinear Localized Strain Waves in Generalized Continua
The basic principles of structural modeling for the construction of mathematical models of microstructured media (generalized continua) are given. Here, microstructure means not the smallness of absolute value...
-
Chapter
Localized Magnetoelastic Waves in a One and Two Dimensional Medium
The impact of external magnetic field on the generation of localized waves in non-linear conductive rod and plate has been studied. We have obtained evolutionary equations which describe the propagation of one...
-
Chapter
Rotational Waves in Microstructured Materials
A brief review of theoretical representations and experimental data on rotational motions of elements of a continuous medium is given. Description of wave rotational motions is impossible in the framework of t...
-
Chapter
Dispersion Properties of a Closed-Packed Lattice Consisting of Round Particles
A two-dimensional discrete model for a hexagonal (closed-packed) lattice with elastically interacting round particles possessing two translational and one rotational degrees of freedom is considered. The linea...
-
Chapter
Frequency-Dependent Attenuation and Phase Velocity Dispersion of an Acoustic Wave Propagating in the Media with Damages
In frame of the self-consistent mathematical model, which includes the dynamics of a material and the state of its defects, the particular qualities of acoustic wave propagation in the material with damage is ...
