Dynamic frictional contact of a viscoelastic beam
In this paper, we study the dynamic frictional contact of a viscoelastic beam with a deformable obstacle. The beam is assumed to be situated horizontally and to move, in both horizontal and tangential directions, by the effect of applied forces. The left end of the beam is clamped and the right one is free. Its horizontal displacement is constrained because of the presence of a deformable obstacle, the so-called foundation, which is modelled by a normal compliance contact condition. The effect of the friction is included in the vertical motion of the free end, by using Tresca's law or Coulomb's law. In both cases, the variational formulation leads to a nonlinear variational equation for the horizontal displacement coupled with a nonlinear variational inequality for the vertical displacement. We recall an existence and uniqueness result. Then, by using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives, a numerical scheme is proposed. Error estimates on the approximative solutions are derived. Numerical results demonstrate the application of the proposed algorithm.
Numerical analysis of a quasi-static contact problem for a thermoviscoelastic beam
In this paper we revisit a quasi-static contact problem of a thermoviscoelastic beam between two rigid obstacles which was recently studied in [1]. The variational problem leads to a coupled system, composed of an elliptic variational inequality for the vertical displacement and a linear variational equation for the temperature field. Then, its numerical resolution is considered, based on the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. Error estimates are proved from which, under adequate regularity conditions, the linear convergence is derived. Finally, some numerical simulations are presented to show the accuracy of the algorithm and the behavior of the solution.
Accurate measurements of output characteristics and detonations of motorbike high-speed racing engine and their optimization at actual atmospheric conditions and combusted mixture composition
Abstract At a motorbike high speed racing engine there is very important an output engine characteristics which depends significantly on a detonation combustion rate, atmospheric conditions and a combusted mixture composition. The combustion process has got a relevant influence on a wear degree of main engine parts or on their damage eventually. The detonation combustion rate is very important because this kind of burning can be not only destructive but a useful phenomenon, as well. If the process of detonation burning is kept on a certain level, it can help significantly to the next increasing of an engine power output. In this article there is described the measurements of output characteristics of a high-speed racing engine which were performed by means of a data-recording system and the detonation combustion was evaluated using a quantitative method. The actual values of atmospheric conditions and the mixture composition were added to the measured values. Then the obtained values are compared visually with a damage degree of an engine piston caused by the detonation burning. The result is a limit value expressed in a number of detonation units related to a run distance interval of the vehicle driven by the high-speed racing engine. In framework of this run distance interval there is the process of detonation burning profitable. As well as it increases an engine power output and together it is not destructive with regard to engine design parts.