The computational procedure for investigation vibration stability of a flexible rotor consisting of an asymmetric shaft, one disc, and supported by ball bearings is developed in this work. Lagrange equations of the second kind were used for derivation of the motion equation. The vibration response stability of the Jeffcott-like rotor was studied by means of eigenvalues of a transition matrix. Three different methods for approximation of the transition matrix have been investigated. The presented simulations are focused on studying the influence of parametric excitation produced by the shaft asymmetry and self-excitation vibration caused by the shaft material damping. The numerical results proved the applicability of the developed procedure, which has been verified by the direct integration of the motion equation.
Jan Poduška, Pavel Hutař, Andreas Frank, Jaroslav Kučera, Jiří Sadílek, Gerald Pinter and Luboš Náhlík
Lifetime of plastic pipes can be estimated by integration of a power law describing the crack kinetics. However, this procedure requires an FEM (finite element method) calculation of the possible crack propagation in the pipe to obtain stress intensity factor dependency on the crack length. It is very important for the simulation to consider every possible load that is acting on the pipe. This contribution deals with FEM modelling of a pipe that is loaded by internal pressure, residual stresses and soil loads. Comparison of the factors and pipe lifetime estimation is carried out.
The application of first order shear beam theory in the analysis of beam structures made of functionally graded materials requires the access to homogenized stiffness quantities. These quantities depend on the cross-sectional shape and on the spatial variation of constitutive parameters. Some of these stiffness quantities can be evaluated easily by simple integration, however, the access to transverse shear stiffnesses and to stiffness quantities regarding warping torsion is typically cumbersome. In this contribution a novel approach for their evaluation is proposed, which is based on a reference beam problem. Here, we restrict ourselves to double symmetric cross-sections, however, a generalization of the proposed method to the arbitrary case is obvious. Besides that, a novel approach to cover non-uniform warping torsion is included. The proposed method is efficient, since the discretization of the cross-section suffices, and accurate as can be shown in challenging bench mark problems.
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Mechanical Engineering, VŠB-Technical University of Ostrava, Ostrava, Czech Republic, 2016, pp. 1-264.
 Hoschl, C., Okrouhlik, M. Solution of Systems of Nonlinear Equations. Journal of Mechanical Engineering, ISSN 0039-2472, vol. 54, 4, 2003, Slovakia, pp. 197-227.
 Jančo, R. Solution of Thermo-Elastic-Plastic Problems with Consistent Integration of Constitutive Equations. Journal of Mechanical Engineering, ISSN 0039-2472, vol. 53, 4, 2002, Slovakia, pp. 197-214.
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Pjotrs Trifonovs-Bogdanovs, Anastasia Zhiravetska, Tatjana Trifonova-Bogdanova and Konstantin Mamay
] I. B. Vaisgant, Principles of Inertial Navigation Systems Structure . Saint Petersburg: LETI, 1984.
 M. S. Grewal, L. R. Weill, and A. P. Andrews, Global Positioning Systems, Inertial Navigation, and Integration, Wiley-Interscience, Hoboken, NJ, USA, 2nd edition, 2007.
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room passively; despite that, the PV cell is cooled down by the fresh air aspired from the room.
There exist several improvements to increase the effectiveness of our solar wall, like the use increases the insolation of surrounding walls to limit the heat losses toward the outside, or the integration of the PCM to prolong the operating time of our wall of storage.
 Utzinger, D. M., Analysis of Building Components Related to Direct Solar Heating of Building, M.S. Thesis, University of Wisconsin, Madison, 1979. Utzinger D. M. Analysis of
Pjotrs Trifonovs-Bogdanovs, Artūrs Levikins, Vadims Kirillovs and Zarif Zabirov
 P. Trifonov-Bogdanov, Inertial Navigation Basics. Riga: RKIIGA, 1984.
 W. Wrigley, W. Hollister and W. Denhard, Gyroscopic Theory, Design and Instrumentation, Cambridge: M.I.T. Press, 1969.
 M, S. Grewal, L. R. Weill and A. P. Andrews, Global Positioning Systems, Inertial Navigation and Integration. New York: Wiley, 2004.
 I. Vaisgant, Inertial Navigation Systems Structure Principles. Saint Petersburg: LETI, 1984.
 P. Bromberg, Inertial Navigation