scholarly journals Microscopic Dynamic Mechanism of Irreversible Thermodynamic Equilibration of Crystals

2021 ◽  
Vol 3 (4) ◽  
pp. 724-730
Author(s):  
A. Yu. Zakharov ◽  
M. A. Zakharov
Keyword(s):  
Initial Conditions ◽  
Stationary Regime ◽  
Irreversible Thermodynamic ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
Dynamic Mechanism ◽  
Harmonic Model ◽  
Free And Forced Vibrations ◽  
Statistical Dynamic ◽  
A Chain

The dynamics of free and forced vibrations of a chain of particles are investigated in a harmonic model taking into account the retardation of interactions between atoms. It is found that the retardation of interactions between particles leads to the non-existence of stationary free vibrations of the crystal lattice. It is shown that in the case of a stable lattice, forced vibrations, regardless of the initial conditions, pass into a stationary regime. A non-statistical dynamic mechanism of the irreversible thermodynamic equilibration is proposed.

scholarly journals Microscopic dynamic mechanism of equilibration in crystals: one-dimensional model

2021 ◽  
Vol 2052 (1) ◽  
pp. 012053
Author(s):  
A Yu Zakharov ◽  
M A Zakharov
Keyword(s):  
External Field ◽  
Dynamic Equilibrium ◽  
Initial Conditions ◽  
Free Vibrations ◽  
Dynamic Mechanism ◽  
Dimensional Model ◽  
Many Body ◽  
One Dimensional ◽  
Statistical Dynamic ◽  
A Chain

Abstract The dynamics of free vibrations of a chain of atoms is investigated taking into account the retardation of interactions. It is shown that all oscillations of the circuit are damped. The dynamics of forced vibrations of this chain of atoms is investigated. It is shown that, regardless of the initial conditions, the system passes into a stationary state of dynamic equilibrium with an external field, which depends both on the properties of the system and on the parameters of the external field. A non-statistical dynamic mechanism of the process of irreversible establishment of the state of thermodynamic equilibrium in both many-body and few-body systems is proposed.

scholarly journals Theoretical and comparative study regarding the Galerkin-Vlasov method use for study the free vibrations of wood flat plate

2010 ◽  
pp. 223-228
Author(s):  
Marius Fetea ◽  
Gabriel Cheregi ◽  
Liana Lustun ◽  
Ildico Smit ◽  
Codruta Lucaci ◽  
...  
Keyword(s):  
19Th Century ◽  
18Th Century ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
Theoretical Studies ◽  
Flat Plates ◽  
Free And Forced Vibrations ◽  
First Results ◽  
Historic Record ◽  
The 19Th Century

As for the historic record of the problem related to the study of flat plates, the first results were out for publishing at the end of the 18th century, the beginning of the 19th century, having Chladni E, Strehlke, Konig, R, Tanaka S, Rayleigh L, Ritz W and later on Gontkevich V, Timoshenko S, Leissa as pioneers. Each of the above mentioned authors have had significant contributions regarding the development of methods in order to solve the plates and establish some rigurous solutions of their differential equations of equilibrium. The making of constructions, machines and different high-perfomance appliances, whose functioning should take place in safety conditions, have required theoretical studies of rich complexity, as well as practical experiments, within which the problem of their free and forced vibrations represent an important category in the respective theme of research.

Free and Forced Vibrations of an Infinitely Long Cylindrical Shell in an Infinite Acoustic Medium

1954 ◽  
Vol 21 (2) ◽  
pp. 167-177
Author(s):  
H. H. Bleich ◽  
M. L. Baron
Keyword(s):  
Surrounding Medium ◽  
Low Frequency ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
Acoustic Medium ◽  
Frequency Range ◽  
Stiffened Shells ◽  
Free And Forced Vibrations ◽  
Water Tables ◽  
Radial Forces

Abstract The paper presents a general method for the treatment of free and forced-vibration problems of infinitely long thin cylindrical shells. Surprisingly simple results are obtained by utilizing the known and tabulated modes of the shell in vacuo as generalized co-ordinates describing the response of the shell. The frequencies of free vibrations of submerged shells are obtained, and the response of the shell and medium to sinusoidally distributed, periodic, radial forces is determined. The results indicate that there is a low-frequency range where no radiation occurs and a high-frequency range where energy is radiated. Free vibration, or resonance in the case of forced vibrations, occurs only in the low-frequency range. The results of the paper may be applied to obtain the response to arbitrarily distributed, periodic, or nonperiodic forces by expanding such forces in Fourier series and/or integrals. The results for free and forced vibrations are discussed in general and for the specific case of steel shells in water. Tables are provided to facilitate numerical computations. With limitations the method is also applicable to ring-stiffened shells, and to the case of a static pressure in the surrounding medium.

On Elastic Continua With Hereditary Characteristics

1951 ◽  
Vol 18 (3) ◽  
pp. 273-279
Author(s):  
Enrico Volterra
Keyword(s):  
Equations Of Motion ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
Degree Of Freedom ◽  
Elastic Media ◽  
Stress Strain ◽  
Radial Vibrations ◽  
Damping Characteristics ◽  
Transverse Vibrations ◽  
Free And Forced Vibrations

Abstract In a previous paper (1) the free and forced vibrations of systems of one degree of freedom with hereditary damping characteristics were discussed. In the present paper the classical equations of motion for elastic media are extended on the basis of the general linear stress-strain law involving hereditary damping. These equations are applied to the case of free radial vibrations of a sphere. Furthermore, the free vibrations of strings, the free transverse vibrations of beams, and the free vibrations of rectangular and circular membranes are studied under the assumption of hereditary damping.

scholarly journals The Process of Stellar Tidal Disruption by Supermassive Black Holes

2021 ◽  
Vol 217 (3) ◽  
Author(s):  
E. M. Rossi ◽  
N. C. Stone ◽  
J. A. P. Law-Smith ◽  
M. Macleod ◽  
G. Lodato ◽  
...  
Keyword(s):  
Black Holes ◽  
Initial Conditions ◽  
Numerical Models ◽  
Binary Star ◽  
Tidal Disruption ◽  
Massive Black Hole ◽  
Accretion Flows ◽  
Simple Order ◽  
Order Of Magnitude ◽  
A Chain

AbstractTidal disruption events (TDEs) are among the brightest transients in the optical, ultraviolet, and X-ray sky. These flares are set into motion when a star is torn apart by the tidal field of a massive black hole, triggering a chain of events which is – so far – incompletely understood. However, the disruption process has been studied extensively for almost half a century, and unlike the later stages of a TDE, our understanding of the disruption itself is reasonably well converged. In this Chapter, we review both analytical and numerical models for stellar tidal disruption. Starting with relatively simple, order-of-magnitude physics, we review models of increasing sophistication, the semi-analytic “affine formalism,” hydrodynamic simulations of the disruption of polytropic stars, and the most recent hydrodynamic results concerning the disruption of realistic stellar models. Our review surveys the immediate aftermath of disruption in both typical and more unusual TDEs, exploring how the fate of the tidal debris changes if one considers non-main sequence stars, deeply penetrating tidal encounters, binary star systems, and sub-parabolic orbits. The stellar tidal disruption process provides the initial conditions needed to model the formation of accretion flows around quiescent massive black holes, and in some cases may also lead to directly observable emission, for example via shock breakout, gravitational waves or runaway nuclear fusion in deeply plunging TDEs.

Nonlinear Free and Forced Vibrations of Symmetric Laminated Panels

2011 ◽  
Vol 471-472 ◽  
pp. 616-621 ◽  
Author(s):  
Alireza Shooshtari ◽  
Soheil Razavi ◽  
Hadi Ghashochi Bargh ◽  
Mohammad Homayoun Sadr-Lahidjani
Keyword(s):  
Perturbation Method ◽  
External Force ◽  
Laminated Composite ◽  
Composite Plates ◽  
Forced Vibrations ◽  
Numerical Results ◽  
Transverse Displacement ◽  
Laminated Composite Plates ◽  
Free And Forced Vibrations ◽  
Laminated Panels

In this paper, free and forced vibrations of symmetric laminated composite plates are studied analytically by using a perturbation method where the analytical results for transverse displacement are compared with the numerical results. The external force is taken to be harmonic in time and having uniform amplitude.

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