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Oscillations in mechanical systems with implicit constitutive relations.
Babováková, Jana ; Pražák, Dalibor (advisor) ; Janovský, Vladimír (referee)
We study a system of differential-algebraic equations, describing motions of a mass-spring-dashpot oscillator by three different forms of implicit constitu- tive relations. For some problems with fully implicit but linear constitutive laws for combined force, we find conditions for solution stability. Assuming monotone relationship between the displacement, velocity and the respective forces, we prove global existence of the solutions. For a linear spring and a dashpot with maximal monotone relationship between the damping force and the velocity, we prove the global existence and uniqueness result. We also solve this problem numerically for Coulomb-like damping term.
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Approximation, numerical realization and qualitative analysis of contact problems with friction
Ligurský, Tomáš ; Haslinger, Jaroslav (advisor) ; Segeth, Karel (referee) ; Rohan, Eduard (referee)
Title: Approximation, numerical realization and qualitative analysis of contact problems with friction Author: Tomáš Ligurský Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Jaroslav Haslinger, DrSc., Department of Numerical Mathe- matics Abstract: This thesis deals with theoretical analysis and numerical realization of dis- cretized contact problems with Coulomb friction. First, discretized 3D static contact prob- lems with isotropic and orthotropic Coulomb friction and solution-dependent coefficients of friction are analyzed by means of the fixed-point approach. Existence of at least one solution is established for coefficients of friction represented by positive, bounded and con- tinuous functions. If these functions are in addition Lipschitz continuous and upper bounds of their values together with their Lipschitz moduli are sufficiently small, uniqueness of the solution is guaranteed. Second, properties of solutions parametrized by the coefficient of friction or the load vector are studied in the case of discrete 2D static contact problems with isotropic Coulomb friction and coefficient independent of the solution. Conditions under which there exists a local Lipschitz continuous branch of solutions around a given reference point are established due to two variants of the...
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Oscillations in mechanical systems with implicit constitutive relations.
Babováková, Jana ; Pražák, Dalibor (advisor) ; Janovský, Vladimír (referee)
We study a system of differential-algebraic equations, describing motions of a mass-spring-dashpot oscillator by three different forms of implicit constitu- tive relations. For some problems with fully implicit but linear constitutive laws for combined force, we find conditions for solution stability. Assuming monotone relationship between the displacement, velocity and the respective forces, we prove global existence of the solutions. For a linear spring and a dashpot with maximal monotone relationship between the damping force and the velocity, we prove the global existence and uniqueness result. We also solve this problem numerically for Coulomb-like damping term.
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Bifurcations in contact problems with Coulomb friction
Ligurský, Tomáš ; Renard, Y.
To explore the bifurcation in this contact problem, we have taken uniform meshes with 4096, 16384, 65536 and 262144 triangles. We shall show that the bifurcation behaviour is more complex here. Branches 1 and 4 approach one another for finer meshes, and they disappear both for the finest mesh. Nevertheless, regarding the branching of the corresponding contact problem with forces h = (h1,h2) over the plane h1-h2, one can find it stable and convergent, again. \n
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Experimental investigation of coarse particle conveying in pipes
Vlasák, Pavel ; Chára, Zdeněk ; Konfršt, Jiří ; Krupička, Jan
The advanced knowledge of particle-water mixture flow behaviour is important for safe, reliable, and economical design and operation of the freight pipelines. The effect of the mixture velocity and concentration on the coarse particle – water mixtures flow behaviour was experimentally investigated on an experimental pipe loop of inner diameter D = 100 mm with horizontal, vertical, and inclined pipe sections. Narrow particle size distribution basalt pebbles were used as model of coarse-grained solid particles. The radiometric method was used to measure particle concentration distribution in pipe cross-section. Mixture flow behaviour and particles motion along the pipe invert were studied in a pipe viewing section. The study revealed that the coarse particlewater mixtures in the horizontal and inclined pipe sections were significantly stratified. The particles moved principally in a layer close to the pipe invert. However, for higher and moderate flow velocities the particles moved also in the central part of the pipe cross-section, and particle saltation was found to be dominant mode of particle conveying.
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