143 research outputs found
Boundary value problems of elasticity theory for plane domains with one-dimensional elastic reinforcements
This article is a translation of an article published in Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No 1, pp 103-114 Jan-Feb 1991.Many authors have examined problems related to the load transmission from an elastic rod to an elastic plane. It was assumed in the majority of investigationa that the stringer is a thin rectilinear rod transmitting only longitudinal forces while the rod contact with the plane is realized along a line. different modifications of sheet contact with a rectilinear tensile stringer considered as an inner stringer of finite length or as an infinite edge stringer were analyzed in [1, 2]. Problems about the reinforcement of holes in a plate by a thin rod of constant section that possesses bending and longitudinal stiffnesses were solved in [3]. The eccentricity of the connection between the shell middle surface and the rod was taken into account in [4] in a study of shells reinforced by thin curvilinear rods. Other models of the one-dimensional element connected to an elastic medium without taking account of its bending stiffness were analyzed in [5, 6]. Solutions of a number of problems with circular reinforcing elements are obtained in [7]. An isotropic finite or infinite, linearly elastic plate reinforced along part or all of the boundary and along certain internal lines by elastic curvilinear rods possessing variable longitudinal and bending stiffnesses, variable curvature and thickness, the eccentricity of the connection to the plate and with an arbitrary transverse section shape symmetric relative to the plate middle surface are studied in this paper. Boundary conditions on the line of plate contact with the inner or edge elastic rods are obtained for the reinforcement models generalizing [1, 2] by using the theory of elastic rods in the case of a plane state of stress. Existence and uniqueness theorems are proved for appropriate boundary value problems; the singularity of the stresses at angles and tips of the rods are proved. The relationships obtained carry over completely to the plane strain problem for an elastic cylinder reinforced by homogeneous cylindrical shells along the generator. Some of the results described here are represented in [8]
Stable periodic waves in coupled Kuramoto-Sivashinsky - Korteweg-de Vries equations
Periodic waves are investigated in a system composed of a
Kuramoto-Sivashinsky - Korteweg-de Vries (KS-KdV) equation, which is linearly
coupled to an extra linear dissipative equation. The model describes, e.g., a
two-layer liquid film flowing down an inclined plane. It has been recently
shown that the system supports stable solitary pulses. We demonstrate that a
perturbation analysis, based on the balance equation for the field momentum,
predicts the existence of stable cnoidal waves (CnWs) in the same system. It is
found that the mean value U of the wave field u in the main subsystem, but not
the mean value of the extra field, affects the stability of the periodic waves.
Three different areas can be distinguished inside the stability region in the
parameter plane (L,U), where L is the wave's period. In these areas, stable
are, respectively, CnWs with positive velocity, constant solutions, and CnWs
with negative velocity. Multistability, i.e., the coexistence of several
attractors, including the waves with several maxima per period, appears at
large value of L. The analytical predictions are completely confirmed by direct
simulations. Stable waves are also found numerically in the limit of vanishing
dispersion, when the KS-KdV equation goes over into the KS one.Comment: a latex text file and 16 eps files with figures. Journal of the
Physical Society of Japan, in pres
Localized structures of electromagnetic waves in hot electron-positronplasmas
The dynamics of relativistically strong electromagnetic (EM) wave propagation
in hot electron-positron plasma is investigated. The possibility of finding
localized stationary structures of EM waves is explored. It is shown that under
certain conditions the EM wave forms a stable localized soliton-like structures
where plasma is completely expelled from the region of EM field location.Comment: 14 pages, LaTeX, 1 figure can be obtained upon request through email
to [email protected]
Negative differential resistivity in superconductors with periodic arrays of pinning sites
We study theoretically the effects of heating on the magnetic flux moving in
superconductors with a periodic array of pinning sites (PAPS). The
voltage-current characteristic (VI-curve) of superconductors with a PAPS
includes a region with negative differential resistivity (NDR) of S-type (i.e.,
S-shaped VI-curve), while the heating of the superconductor by moving flux
lines produces NDR of N-type (i.e., with an N-shaped VI-curve). We analyze the
instability of the uniform flux flow corresponding to different parts of the
VI-curve with NDR. Especially, we focus on the appearance of the filamentary
instability that corresponds to an S-type NDR, which is extremely unusual for
superconductors. We argue that the simultaneous existence of NDR of both N- and
S-type gives rise to the appearance of self-organized two-dimensional dynamical
structures in the flux flow mode. We study the effect of the pinning site
positional disorder on the NDR and show that moderate disorder does not change
the predicted results, while strong disorder completely suppresses the S-type
NDR.Comment: 10 pages, 1 table, 7 figure
Plasma instability and amplification of electromagnetic waves in low-dimensional electron systems
A general electrodynamic theory of a grating coupled two dimensional electron
system (2DES) is developed. The 2DES is treated quantum mechanically, the
grating is considered as a periodic system of thin metal strips or as an array
of quantum wires, and the interaction of collective (plasma) excitations in the
system with electromagnetic field is treated within the classical
electrodynamics. It is assumed that a dc current flows in the 2DES. We consider
a propagation of an electromagnetic wave through the structure, and obtain
analytic dependencies of the transmission, reflection, absorption and emission
coefficients on the frequency of light, drift velocity of 2D electrons, and
other physical and geometrical parameters of the system. If the drift velocity
of 2D electrons exceeds a threshold value, a current-driven plasma instability
is developed in the system, and an incident far infrared radiation is
amplified. We show that in the structure with a quantum wire grating the
threshold velocity of the amplification can be essentially reduced, as compared
to the commonly employed metal grating, down to experimentally achievable
values. Physically this is due to a considerable enhancement of the grating
coupler efficiency because of the resonant interaction of plasma modes in the
2DES and in the grating. We show that tunable far infrared emitters, amplifiers
and generators can thus be created at realistic parameters of modern
semiconductor heterostructures.Comment: 28 pages, 15 figures, submitted to Phys. Rev.
Estimates of the influence of the transverse strain in a contact problem with free boundary
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