Vibrations analysis of a mechanical system consisting of two identical parts
Keywords:
vibration, symmetrical system, identical parts, eigenvaluesAbstract
In many technical applications (like those in automotive engineering or in structural mechanics) the mechanical system studied can be considered composed by two or many identical subsystems or parts. These kind of symmetries of the structure can be used in order to simplify the analysis of the vibrations and permit to reduce the dimension of the differential equations that describe the motion. In the paper we proof that in case of such technical systems with elastic elements composed of two identical subsystems, the eigenvalues of the subsystems associated to the identical parts are eigenvalues of the whole structure as well. The demonstrated property allows the simplification of the calculation of the problem of eigenvectors and eigenvalues for this kind of structure.
References
VLASE, S., A method of eliminating Lagrangian multipliers from the equation of motion of interconnected mechanical systems, ASME Transaction ? Journal of Applied Mechanics, 54, 1, pp. 235?237, 1987.
MEIROVITCH, L., Elements of vibration analysis (2nd ed.), McGraww-Hill, New York, 1970.
VLASE, S., Elimination of Lagrangian multipliers, Mechanics Research Communications, 14, 1, pp. 17?22, 1987.
NICOAR?, D., SECAR?, E., MIH?LCIC?, M., Study of rotor-bearing systems using Campbell diagram, Proceedings of the 1st International Conference on Manufacturing Engineering, Quality and Production Systems (MEQAPS’09), Volume II, Bra?ov, Romania, 2009, pp. 393?396.
MANGERON, D., GOIA, I., VLASE, S., Symmetrical branched systems vibration, Memoirs of the Scientific Sections of the Romanian Academy, Series IV, XII, 1, 1991.
VLASE, S., TEODORESCU-DR?GHICESCU, H., SCUTARU, L.M., On the eigenvalues of the elastic systems with some symmetries, 6th International DAAAM Baltic Conference ? Industrial Engineering, Tallinn, Estonia, 2008.
STAICU, ?t., Dynamics analysis of a two-module hybrid parallel manipulator, Ro. J. Techn. Sci. ? Appl. Mechanics, 59, 3, pp. 293?303, 2014.
STAICU, ?t., OCNARESCU, C., UNGUREANU,L., Dynamics modelling of a parallel flight simulator, Ro. J. Techn. Sci. ? Appl. Mechanics, 58, 3, pp. 273?285, 2013.
VLASE, S., TEODORESCU, P.P., ITU, C., SCUTARU, M.L., Elasto-dynamics of a solid with a general “rigid” motion using FEM model. Part II. Analysis of a double cardan joint, Romanian Journal of Physics, 58, 7–8, pp. 882–892, 2013.
VLASE, S., D?N??EL, C., SCUTARU, M.L., MIH?LCIC?, M., Finite Element Analysis of a two-dimensional linear elastic systems with a plane “rigid motion”, Romanian Journal of Physics, 59, 5–6, pp. 476–487, 2014.
SCUTARU, M.L., VLASE, S., Some properties of motion equations describing the nonlinear dynamical response of a multibody system with flexible elements, Journal of Applied Mathematics, doi:10.1155/2012/628503, 2012.
HORN, R.A., JOHNSON, Ch.R., Matrix Analysis, Cambridge University Press, 1985.
HARIS, C.M., CREDE, C.E., Shock and vibration handbook (2nd ed.), McGraw-Hill, 1976.
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