Machines and machines aggregates' stability problems theoretical and experimental investigations. L Dynamic machining systems stability.
Mathematical formulation of fluid-structure interaction problems
Mathematical modelling of cable stayed bridges: existence, uniqueness, continuous dependence on data, homogenization of cable systems
A model of a cable stayed bridge is proposed. This model describes the behaviour of the center span, the part between pylons, hung on one row of cable stays. The existence, the uniqueness of a solution of a time independent problem and the continuous dependence on data are proved. The existence and the uniqueness of a solution of a linearized dynamic problem are proved. A homogenizing procedure making it possible to replace cables by a continuous system is proposed. A nonlinear dynamic problem connected...
Mathematical modelling of ultrasonic non-destructive evaluation.
Mathematical models of suspension bridges
In this work we try to explain various mathematical models describing the dynamical behaviour of suspension bridges such as the Tacoma Narrows bridge. Our attention is concentrated on the derivation of these models, an interpretation of particular parameters and on a discussion of their advantages and disadvantages. Our work should be a starting point for a qualitative study of dynamical structures of this type and that is why we have a closer look at the models, which have not been studied in literature...
Mathematical study of an evolution problem describing the thermomechanical process in shape memory alloys
In this paper we prove existence, uniqueness, and continuous dependence for a one-dimensional time-dependent problem related to a thermo-mechanical model of structural phase transitions in solids. This model assumes the free energy depending on temperature, macroscopic deformation and also on the proportions of the phases. Here we neglect regularizing terms in the momentum balance equation and in the constitutive laws for the phase proportions.
Maximal regularity for flexible structural systems in Lebesgue spaces.
Mixed formulation for elastic problems - existence, approximation, and applications to Poisson structures
A mixed formulation is given for elastic problems. Existence and uniqueness of the discretized problem are given for conformal continuous interpolations for the stress tensor components and for the components of the displacement vector. A counterpart of the problem is discussed in the case of an even-dimensional Euclidean space with an associated Hamiltonian vector field and the Poisson structure. For conformal interpolations of the same order the question remains open.
Mixed interface problems for anisotropic elastic bodies.
Modal formulation of segmented Euler-Bernoulli beams.
Model validation using coordinate distance with performance sensitivity.
Modeling the tip-sample interaction in atomic force microscopy with Timoshenko beam theory
A matrix framework is developed for single and multispan micro-cantilevers Timoshenko beam models of use in atomic force microscopy (AFM). They are considered subject to general forcing loads and boundary conditions for modeling tipsample interaction. Surface effects are considered in the frequency analysis of supported and cantilever microbeams. Extensive use is made of a distributed matrix fundamental response that allows to determine forced responses through convolution and to absorb non-homogeneous...
Modeling the vibrations of a multi-rod structure
Moving Griffith crack in an orthotropic strip with punches at boundary faces.