oupled transversal and longitudinal vibrations of a plane mechanical system with two identical beams
Keywords:vibration, eigenvalue, eigenmode, beam, symmetry
The paper aims to highlight some vibrations properties for a plane beams structure, where transverse vibrations are coupled with the longitudinal vibrations. In engineering practice it often happens that identical parts are used in projects for reasons which relate to design time, material costs and execution time. Considering only the statics approach, these types of systems have been studied in strength of materials. In the case of dynamics, some comments on the calculation of symmetrical systems have been made in the literature, but a systematic study does not yet exist; some particular cases were treated in the literature. In this paper we aim to study a symmetrical system of beams that presents vibrations in the system’s plane. The determination of properties of such systems would decrease the computational time and effort and would automatically imply lower development and testing costs and would increase the accuracy of calculus.
MEIROVITCH, L., Principles and Techniques of Vibrations, Pearson, 1996.
MANGERON, D., GOIA, I., VLASE, S., Symmetrical branched systems vibrations, Scientific Memoirs of the Romanian Academy, Bucharest, Serie IV, XII, 1, pp. 232?236, 1991.
VLASE, S., CHIRU, A., Simmetry in the study of the vibration of some engineering mechanical systems, Proceedings of the 3rd International Conference on Experiments/ Process/ System Modeling/ Simulation/ Optimization (3rd IC-EpsMsO), Athens, Greece, July 8–11, 2009.
SHI, C.Z., PARKER, R.G., Modal structure of centrifugal pendulum vibration absorber systems with multiple cyclically symmetric groups of absorbers, Journal of Sound and Vibration, 332, 18, pp. 4339?4353, 2013.
PALIWAL, D.N., PANDEY, R.K., Free vibrations of circular cylindrical shell on Winkler and Pasternak foundations, International Journal of Pressure Vessels and Piping, 69, 1, pp. 79?89, 1996.
CELEP, Z., On the axially symmetric vibration of thick circular plates, Archive of Applied Mechanics, 47, 6, pp 411?420, 1978.
BUZDUGAN, GH., FETCU, L., RADES, M., Mechanical vibrations, Editura Didactic? ?i Pedagogic?, Bucharest, 1982.
DOUGLAS, Th., Structural dynamics and vibrations in practice: an engineering handbook, CRC Press, 2012.
TIMOSHENKO, P.S., GERE, J.M., Theory of elastic stability, McGraw-Hill, 2nd Edition, 2009.
MYINT-U, T., Ordinary differential equations, Elsevier, 1977.
HENDERSON, J., LUCA, R., Boundary value problems for systems of differential, difference and fractional equations: positive solutions, Elsevier, 2016.
SHARMA, K., MARIN, M., Effect of distinct conductive and thermodynamic temperatures on the reflection of plane waves in micropolar elastic half-space, U.P.B. Sci. Bull., Series A-Appl. Math. Phys., 75, 2, pp. 121?132, 2013.
MARIN, M., LUPU, M., On harmonic vibrations in thermoelasticity of micropolar bodies, Journal of Vibration and Control, 4, 5, pp. 507?518, 1998.
MARIN, M., A domain of influence theorem for microstretch elastic materials, Nonlinear analysis: RWA, 11, 5, pp. 3446?3452, 2010.
VLASE, S., PAUN, M., Vibration analysis of a mechanical system consisting of two identical parts, Ro. J. Techn. Sci. ? Appl. Mechanics, 60, 3, pp. 216?230, Bucharest, 2015.
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