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References [1] Caughey, T. K., O’Kelly, M. E. J.: Classical Normal Modes in Damped Linear Dynamic System. Transaction of the ASME. Journal of Applied Mechanics 32, 1965. pp:583-588. [2] Caughey, T. K.: Classical Normal Modes in Damped Linear Dynamic System. Transaction of the ASME. Journal of Applied Mechanics June. 1960. pp:269-271. [3] Fawzy, T. K.: A Theorem on the Free Vibration of Damped System. Transaction of the ASME. Journal of Applied Mechanics Marc. 1977. pp:132-134. [4] Sas, P., Ward, H., Lammens, S.: Modal Analysis Theory and Testing. Katholike

BIBLIOGRAPHY 1. Chakrabarti S., EMPIRICAL CALCULATION OF ROLL DAMPING FOR SHIPS AND BARGES, Ocean Engineering, Volume 28, Issue 7, pp. 915-932, 2001. 2. Chen J.P., Zhu D.X, NUMERICAL SIMULATIONS OF WAVE-INDUCED SHIP MOTIONS IN TIME DOMAIN BY A RANKINE PANEL METHOD, Journal of Hydrodynamics, Ser. B, Volume 22, Issue 3, pp. 373-380, 2010. 3. Dudziak J., TEORIA OKRĘTU. Wydawnictwo Morskie, Gdańsk 1988. 4. Dymarski P. Dymarski Cz., COMPUTATIONAL MODEL FOR SIMULATION OF LIFEBOAT MOTIONS DURING ITS LAUNCHING FROM SHIP IN ROUGH SEAS, Polish Maritime Research Vol. 19 No

Reference Avedesian, M.M., Baker, H., 1999. Magnesium and Magnesium Alloys , Materials Park OH: ASM International, 298. Braszczyńska-Malik, K.N., 2009. Discontinuous and continuous precipitation in magnesium aluminium type alloys , Journal of Alloys and Compounds, 477, 870-876. Göken, J., Swiostek, J., Letzig, D., Kainer, K.U., 2005. Damping measurements of the magnesium wrought alloys AZ31, AZ61 and AZ80 after in-direct and hydrostatic extrusion , Materials Science Forum, 482, 387-390. Hao, G.L., Han, F.S., Wang, Q.Z., Wu, J., 2007. Internal friction peaks

. Vnútorné tlmenie materiálov , Žilina: EDIS. 5. S challer R., F antozzi G., G remaud G. 2001. Mechanical spectroscopy Q -1 2001 with applications to materials science. Switzerland Trans Tech Publications, pp. 683. 6. Z hang Z., Z eng X., D ing W. 2005. The influence of heat treatment on damping response of AZ91D magnesium alloy. In: Materials Science and Engineering, vol. 392, issues 1 – 2 pp. 150 - 155.

References 1. Chakrabarti, S. Empirical calculation of roll damping of ships and barges, Ocean Engineering, Vol. 28, pp. 915-932, 2001. 2. Cueva, M, Hansen, AS, Silva, JLB, Faria, F, Morato, A. HYDRODYNAMICS OF AN INSTALATION BARGE WITH BILGE KEELS AND STINGER, 29th ASME International Conference on Ocean, Offshore and Arctic Engineering, Shanghai, PEOPLES R CHINA, JUN 06-11, 2010. 3. D. Mylonas, P. Sayer. The hydrodynamic flow around a yacht keel based on LES and DES, Ocean Engineering, Vol. 46, pp. 18-32, 2012. 4. Dai, CM, Miller, RW, Percival, AS. HYDRODYNAMIC

order to improve the quality of the cutting process. Annals of the University of Petroşani, Mechanical Engineering, 20, pp. 63-72. Kurowski, P.M. (2016). Vibration Analysis with SOLIDWORKS® Simulation. Mission: SDC Publications. C. T. Sun, J. N. Juang (1985), - Modeling Global Structural Damping in Trusses Using Simple Continuum Models, AIAA JOURNAL, VOL. 24, NO. 1, pp. 144-150; Kurowski, P. M. (2015). Engineering Analysis with SOLIDWORKS® Simulation. Mission: SDC Publications.

Abstract

The purpose of this paper is to justify that it is necessary to take account of physical and mechanical properties of soil and different materials of erected structure for damping vibrations in dynamic loads; to suggest tools for modelling the damping effect (natural or engineering induced) between foundation and soil. Certain technique is suggested for modelling behaviour of structure in time history analysis with account of material damping. In the software, the damping effect is modelled in two variants: Rayleigh damping (for structure) and finite element of viscous damping. When solving this problem, the following results were obtained: physical meaning of material damping is described; Rayleigh damping coefficients were computed through modal damping coefficients. Numerical analysis is carried out for the structure together with soil in earthquake load using developed FE of viscous damping. Time history analysis was carried out for the problem. Peak values of displacement, speed and acceleration at the floor levels were compared. Analysis results are compared (with and without account of material damping). Significant influence of damping on the stress-strain state of the structure is confirmed. Scientific novelty of the paper is in the following: the damping effect is proved to happen regardless of the presence of installed structural damping equipment; technique for account of damping with Rayleigh damping coefficients is developed; new damping element is developed – FE of viscous damping (FE 62), its behaviour is described as linear mathematical model. Practical implications of the paper: developed technique and new FE enables the user to carry out numerical analysis properly and work out a set of measures on seismic safety for buildings and structures.

References [1] Alisjarbana S.W and Wangsadinata W. (2007): Dynamic Response of damped orthotropic plate on Pasternak foundation to dynamic moving loads. - Proceeding of ISEC-4, Melbourne, Australia, 1037-1041. [2] Fryba L. (1999): Vibration of solids and structures under moving loads. - Prague: Research Institute of Transport. [3] Gbadeyan J.A. and Dada M.S. (2001): The dynamic response of plates on Pasternak foundation to distributed moving loads. - Journal of Nigerian Mathematical Physics, vol.5, pp.185-200. [4] Gbadeyan J.A., Idowu A.S., Dada M.S. and Titiloye

proc. of International RILEM Conference on Dynamic Behavior of Concrete Structures , September, Expertcentrum TU Košice. Králik, J. and Cesnak, J. (2006) Experimental and numerical reliability analysis of damping devices under impact loads from container. In: First European Conference on Earthquake Engineering and Seismology. Abstract Book. 3-8 September, Geneva, Switzerland. pp. 256. Králik, J. (2009) Safety and Reliability of Nuclear Power Buildings in Slovakia. Earthquake - Impact - Explosion. Ed. STU Bratislava, 307 pp. Malý, J., Štepán, J., Schererová, K

References [1] SAUER, P. W.-PAI, M. A. KUNDUR: Power System Dynamics and Stability, Prentice Hall, 1998. [2] ROGERS, G. : Power System Oscillations, Kluwer Academic Publishers, 2000. [3] WATSON, W.-MANCHUR, G. : Experience with Supplementary Damping Signals for Generator Static Excitation Systems, IEEE Trans. PAS, 92 (Jan 1973), 199-203. [4] KLEIN, M.et al : A Fundamental Study of Inter-area Oscillations in Power Systems, IEEE Trans. on Power Systems 6 No. 3 (Aug.1991), 914-921. [5] KLEIN, M.et al : Analytical Investigation of Factors Influencing Power System