scholarly journals Another Special Case of Vibrations of a Rolling Tire

2020 ◽  
Vol 16 (4) ◽  
pp. 531-542
Author(s):  
I.F. Kozhevnikov ◽  
Keyword(s):  
Differential Equation ◽  
Angular Velocity ◽  
Rare Case ◽  
Ground Plane ◽  
Steady State Regime ◽  
Quartic Polynomial ◽  
State Regime ◽  
Undeformed State ◽  
Incompressible Rubber ◽  
Special Case

We investigate a special case of vibrations of a loaded tire rolling at constant speed. A previously proposed analytical model of a radial tire is considered. The surface of the tire is a flexible tread combined with elastic sidewalls. In the undeformed state, the tread is a circular cylinder. The tread is reinforced with inextensible cords. The tread is the part of the tire that makes actual contact with the ground plane. In the undeformed state, the sidewalls are represented by parts of two tori and consist of incompressible rubber described by the Mooney –Rivlin model. The previously obtained partial differential equation which describes the tire radial in-plane vibrations about steady-state regime of rolling is investigated. Analyzing the discriminant of the quartic polynomial, which is the function of the frequency of the tenth degree and the function of the angular velocity of the sixth degree, the rare case of a root of multiplicity three is discovered. The angular velocity of rotation, the tire speed and the natural frequency, corresponding to this case, are determined analytically. The mode shape of vibration in the neighborhood of the singular point is determined analytically.

scholarly journals Steady states of the reaction-diffusion equations. Part 1: Questions of existence and continuity of solution branches

1983 ◽  
Vol 24 (4) ◽  
pp. 374-391 ◽  
Author(s):  
J. G. Burnell ◽  
A. A. Lacey ◽  
G. C. Wake
Keyword(s):  
Existence Of Solutions ◽  
Reaction Diffusion ◽  
Elliptic Partial Differential Equations ◽  
Reaction Diffusion Equations ◽  
Steady State Regime ◽  
Nonlinear Elliptic ◽  
Minimal And Maximal Solutions ◽  
Exothermic Chemical Reaction ◽  
State Regime ◽  
Special Case

AbstractWhen material is undergoing an exothermic chemical reaction which is sustained by the diffusion of a reactant, the steady-state regime is governed by a coupled pair of nonlinear elliptic partial differential equations with linear boundary conditions. In this paper we consider questions of existence of solutions to these equations. It is shown that, with the exception of the special case in which the mass-transfer is uninhibited on the boundary, a solution always exists, whereas in this special case a solution exists only for sufficiently low values of the exothermicity. Bounds are established for the solutions and the occurrence of minimal and maximal solutions is shown for some cases. Finally the behaviour of the solution set with respect to one of the parameters is studied.

Dissipative and Generative Fractional Electric Elements in Modeling RC and RL Circuits

2021 ◽  
Author(s):  
Kristian Haška ◽  
Stevan Cvetićanin ◽  
Dušan Zorica
Keyword(s):  
Asymptotic Behavior ◽  
Steady State ◽  
Constitutive Equation ◽  
Magnetic Flux ◽  
Electromotive Force ◽  
Constitutive Models ◽  
Steady State Regime ◽  
Power Type ◽  
State Regime ◽  
Transient And Steady State

Abstract Generalized capacitor (inductor) is constitutively modeled by expressing charge (magnetic flux) in terms of voltage (current) memory as a sum of instantaneous and power type hereditary contributions and it is proved to be a dissipative electric element by thermodynamic analysis. On the contrary, generalized capacitor (inductor) as a generative electric element is modeled using the same form of the constitutive equation, but by expressing voltage (current) in terms of charge (magnetic flux) memory. These constitutive models are used in transient and steady state regime analysis of the series RC and RL circuits subject to electromotive force, as well as in the study of circuits' frequency characteristics including asymptotic behavior.

scholarly journals On the mathematical model of combined rarefaction and compression waves in condensed matter

2021 ◽  
Vol 50 ◽  
pp. 104-107
Author(s):  
Alexander Alexandrovitch Samokhin ◽  
Pavel Aleksandrovich Pivovarov
Keyword(s):  
Shock Wave ◽  
Rarefaction Wave ◽  
Condensed Matter ◽  
Steady State Regime ◽  
Compression Waves ◽  
Momentum Fluxes ◽  
State Regime ◽  
The Mathematical Model ◽  
The Waves ◽  
Nonmetal Transition

Two waves model where shock wave is combined with rarefaction wave appearing in laser ablation due to metal-nonmetal transition effect is investigated using conservation laws for mass and momentum fluxes for the steady-state regime of the process. This approach permits to obtain the relation between front velocities of the waves which shows that the rarefaction wave can be rather slow compared with the generated shock wave.

scholarly journals Simulation of a two-dimensional binary gas mixture outflow into vacuum through a thin slit on the basis of direct solution of the Boltzmann kinetic equation

2021 ◽  
Vol 2056 (1) ◽  
pp. 012007
Author(s):  
S S Sitnikov ◽  
F G Tcheremissine ◽  
T A Sazykina
Keyword(s):  
Kinetic Equation ◽  
Boltzmann Kinetic Equation ◽  
Gas Mixture ◽  
Two Dimensional ◽  
Direct Solution ◽  
Steady State Regime ◽  
Collision Integrals ◽  
Flow Formation ◽  
Binary Gas Mixture ◽  
State Regime

Abstract Two-dimensional binary gas mixture outflow from a vessel into vacuum through a thin slit is studied on the basis of direct solution of the Boltzmann kinetic equation. For evaluation of collision integrals in the Boltzmann equation a conservative projection method is used. Numerical simulation of a two-dimensional argon-neon gas mixture outflow from a vessel into vacuum was performed. Graphs of mixture components flow rate dependence on time during the flow formation, as well as fields of molecular density and temperature for steady-state regime, were obtained.

Integrated modelling of DEMO-FNS current ramp-up scenario and steady-state regime

2015 ◽  
Vol 55 (6) ◽  
pp. 063007 ◽  
Author(s):  
A.Yu. Dnestrovskij ◽  
B.V. Kuteev ◽  
A.S. Bykov ◽  
A.A. Ivanov ◽  
V.E. Lukash ◽  
...  
Keyword(s):  
Steady State ◽  
Integrated Modelling ◽  
Steady State Regime ◽  
Current Ramp ◽  
State Regime
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