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Abstrakty
The nonlinear dynamics of a three degree of freedom autoparametrical vibration system with two coupled pendulums in the neighborhood internal and external resonances is presented in this work. It was assumed that the main body is suspended by an element characterized by linear elasticity and linear damping force and is excited harmonicaly in the vertical direction. The two pendulums connected by spring are mounted to the main body. It is assumed, that the motion of the pendulums are damped by viscotic resistive forces. Solutions for the system response are presented for specific values of the uncoupled normal frequency. Analytical solutions have been obtained by using multiple scales method. This method is used to construct first-order non-linear ordinary differential equations governing the modulation of the amplitudes and phases. Steady state solutions are computed for selected values of the systems parameters.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
91--101
Opis fizyczny
Bibliogr. 16 poz., wykr.
Twórcy
autor
autor
- Warsaw University of Technology. Institute of Machine Design Fundamentals, dsa@simr.pw.edu.pl
Bibliografia
- Bajaj, A.K., Johnson, J.M., 1990, Asymptotic Techniques and Complex Dynamics in Weakly Non-linear Forced Mechanical System, Int. J. Non-Linear Mechanics, 25, 2/3, 211-226.
- Bajaj, A.K., Chang, S.I. and Johnson, J.M., 1994, Amplitude Modulated Dynamics of a Resonantly Excited Autoparametric Two Degree-of-Freedom System, Nonlinear Dynamics, 5, 433-457.
- Banerjee, B., Bajaj, A.K., Davies, P., 1996, Resonant dynamics of an autoparametric system: a study using higher-order averaging, Int. J. Non-Linear Mechanics, 31, 1, 21-39.
- Nayfeh, A.H., Mook, D.T., 1979, Nonlinear Oscilations, Wiley, New York.
- Nayfeh, A.H., 2000, Nonlinear interactions, Analytical, Computational, and Experimental Methods, Wiley, New York.
- Sado, D., 1997, The energy transfer in nonlinearly coupled two-degree-of-freedom systems (original title in Polish: Przenoszenie energii w nieliniowo sprzężonych układach o dwóch stopniach swobody), Publishing House of the Warsaw University of Technology, Mechanika, 166.
- Sado, D., 2002, The chaotic phenomenons of a system with inertial coupling, Mechanics and Mechanical Engineering, Ed. T. Kapitaniak, Lodz, Poland, 6, 1, 31-43.
- Sado, D., 2004, The Dynamics of a coupled three degree of freedom mechanical system, Mechanics and Mechanical Engineering, 7, 7, 29-40
- Sado, D., Gajos, K., 2005, Applications of the method of multiple scales to three degree of freedom dynamical system with double pendulum, Proceedings of 8th Conference on dynamical Systems Theory and Applications, Lodz, Poland, 157-164.
- Sado, D., Gajos, K., 2006, Effect of damping on the periodic and chaotic vibration of system with double pendulum, Proceedings of ESDA2006, 8th Biennial ASME Conference on Engineering Systems Design and Analysis, Torino, Italy, ESDA 2006-95637, 1-7.
- Sado, D., Gajos, K., 2007, Analytical investigation of autoparametric system with pringly coupled pendulums, 9th Conference on Dynamical Systems Theory and Applications, Proceedings, Lodz, 605-612.
- Sado, D., Gajos, K., 2008, Analysis of vibration of three degree of freedom dynamical system with double pendulum, Journal of Theoretical and Applied Mechanics, 46, 1, 141-156.
- Sado, D., Kot, M., 2006, Nonlinear oscillations of a coupled autoparametrical system with ideal and nonideal sources of power, Hindawi Publishing Corporation, Mathematical Problems in Engineering, Vol. 2006, Art.ID 82691, 1-20.
- Tondl, A., Nabergoj, R., 2004, The effect of parametric excitation on self-excited three-mass system. Int. J. Non-Linear Mechanics, 39, 821-832.
- Vyas, A., Bajaj, A.K., 2001, Dynamics of autoparametric vibration absorber using multiple pendulums, Journal of Sound and Vibration, 246, 1, 11 5-135.
- Vyas, A., Bajaj, A.K., 2006, Global dynamics of an autoparametric system with multiple pendulums, Journal of Computational and Nonlinear Dynamics, 1, 35-46
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BWA9-0039-0019