Journal of Computational & Applied Research in Mechanical Engineering (JCARME)
مقاله 6 ، دوره 1، شماره 2 ، فروردین 2012، صفحه 119-128 566.78 K )
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22061/jcarme.2012.32 نویسندگان
Chandan Kumar ؛ Vikas Rastogi Rastogi*
تاریخ دریافت : 22 شهریور 1390 ،
تاریخ بازنگری : 22 دی 1390 ،
تاریخ پذیرش : 27 دی 1390
چکیده This work deals with effects of asymmetric stiffness on the dynamic behaviour of the rotor system. The analysis is presented through an extended Lagrangian Hamiltonian mechanics on the asymmetric rotor system, where symmetries are broken in terms of the rotor stiffness. The complete dynamics of asymmetries of rotor system is investigated with a case study. In this work, a mathematical model is developed considering symmetry breaking of a finite rotor due to stiffness. The natural frequency and amplitude of the rotor are obtained analytically through extended Lagrangian formulation. The asymmetries in rotor are also modeled through bond graph modeling technique for the computational analysis. The simulation result shows a considerable agreement with the analytical results. The limiting dynamics of rotor is shown and analyzed through simulation. کلیدواژهها
Asymmetric stiffness ؛ Umbra-Lagrangian ؛ Umbra-Hamiltonian ؛ Bond graphs
مراجع
[1] D. C. Karnopp, R. C. Rosenberg, and D. L. Margolis, System Dynamics: A Unified Approach , John-Wiley and Sons Inc., USA, (1990).
[2] P. C. Breedveld, and G. Dauphin-Tanguy, Bond Graphs for Engineers , North-Holland, Amsterdam, (1992).
[3] P. Gawthrop, and L. Smith, MetaModeling: Bond graphs and Dynamic Systems , Prentice-Hall, (1996).
[4] B. Vujanovic, “Conservation Laws of Dynamical Systems via d’Alembert’s Principle”, Inter. J. Non-Linear Mech., Vol. 13, pp. 185, (1978).
[5] B. Vujanovic, and S. E. Jones, Variational Methods in Non-Conservative Phenomena , Academic press, Boston, (1989).
[6] Di. Djukic, “A Procedure for Finding First Integrals of Mechanical Systems with Gauge-Variant Lagrangians”, Inter. J. Non-Linear Mech. , Vol. 8, pp. 479, (1973).
[7] Dj. Djukic, and B. Vujanovic, “Noether Theory in Classical Mechanics”, Acta Mech. , Vol. 23, pp. 17, (1975).
[8] D. C. Karnopp, “Lagrange’s Equations for Complex Bond Graph Systems”, Journal of the Dynamic Systems, Measurement, and Control , ASME Trans., Vol. 99, pp. 300-306, (1977).
[9] A. Mukherjee, And A. K. Samantaray, “Umbra-Lagrange’s Equations through Bond Graphs”, Proceedings of International Conference on Bond Graph Modeling and Simulation (ICBGM), Phoenix, Arizona, USA, pp. 168-174, (1997).
[10] E. Noether, “Invariant Variationsprobleme”, Ges. Wiss. Worthington , Vol. 2, pp. 235, (1918).
[11] A. Mukherjee, “Junction Structures of Bond graph Theory from Analytical Mechanics Viewpoint”, Proc. of CISS-1st Conference of International Simulation Societies . Zurich, Switzerland, pp. 661-666, (1994).
[12] F. T. Brown, Engineering System Dynamics , 2nd , CRC, Taylor and Francis, (2007).
[13] A. Mukherjee, “The Issue of Invariants of Motion for General Class of Symmetric Systems through Bond Graph and Umbra-Lagrangian”, Proc. of Int. Conf. of Bond Graph Modelling and Simulation ICBGM’01 , Phoenix, Arizona, USA, pp. 295, (2001).
[14] A. Mukherjee, V. Rastogi, and A. Das Gupta, “A Methodology for finding Invariants of Motion for Asymmetric Systems with Gauge-transformed Umbra Lagrangian Generated by Bond Graphs”, Simulation , Vol. 82, No. 4, pp. 207-226, (2006).
[15] A. Mukherjee, V. Rastogi, and A. Dasgupta, “Revisiting Umbra-Lagrangian-Hamiltonian Mechanics: Its Variational foundation and extension of Noether’s theorem and Poincaré-Cartan Integral”, International Journal of Non-Linear Mechanics , Vol. 46, No. 5, pp. 745-757, (2011).
[16] V. Rastogi, A. Mukherjee, “Conservation laws for gauge-variant Umbra-Lagrangian in Classical mechanics using Bond graphs”, Simulation: Transactions of Society of Modeling and Simulation International , Vol. 87, No. 4, pp. 301-312, (2011).
[17] A. Mukherjee, V. Rastogi, A. Dasgupta, “Extension of Lagrangian-Hamiltonian Mechanics for Continuous Systems –Investigations of Dynamic Internally Damped Rotor Driven through Dissipative Coupling”, Nonlinear Dynamics: Journal of Springer Verlag , Vol. 58, No. 1-2, pp. 107-127, (2009).
[18] A. Mukherjee, V. Rastogi, and A. Das Gupta, “A Study of a Bi-Symmetric Electro mechanical System through Umbra Lagrangian Generated by Bond Graphs and Noether’s Theorem”, Simulation , Vol. 83, No. 9, pp. 611-630, (2007).
[19] S. Hassani, Mathematical Physics , Springer-Verlag, New York, (1999).
[20] J. V. Jose, and E. J. Saletan, Classical Dynamics- A Contemporary Approach , Cambridge University Press, Cambridge, (1998).
[21] A. Mukherjee, and R. Karmakar, R., Modelling and Simulation of Engineering System through Bond Graph , Narosa Publishing House, New Delhi, Reprinted by CRC press for North America and by Alpha Science For Europe,(2000).
[22] J. M. Krodkiewski, Dynamics of Rotors , The University of Melbourne, Australia, (2006).
[23] URL://www.Symbols2000.com, (2000).
[24] A. Mukherjee, and A. K. Samantaray, SYMBOLS-Shakti User’s Manual , High-Tech Consultants, STEP Indian Institute of Technology, Kharagpur, India, (2006).
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