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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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