Short Comments on Self-Synchronization of Two Non-Ideal Sources Supported by a Flexible Portal Frame Structure

Abstract

A practical problem of synchronization of a non-ideal (i.e. when the excitation is influenced by the response of the system) and non-linear vibrating system was posed and investigated by means of numerical simulations. Two rotating unbalanced motors compose the mathematical model considered here with limited power supply mounted on the horizontal beam of a simple portal frame. As a starting point, the problem is reduced to a four-degrees-of-freedom model and its equations of motion, derived elsewhere via a Lagrangian approach, are presented. The numerical results show the expected phenomena associated with the passage through resonance with limited power. Further, for a two-to-one relationship between the frequencies associated with the first symmetric mode and the sway mode, by using the variation of torque constants, the control of the self-synchronization and synchronization (in the system) are observed at certain levels of excitations.

Keywords

Non-ideal source portal plane frame internal resonance

Get full access to this article

View all access options for this article.

References

Balthazar, J. M. , Mook, D. T. , Weber; H. I. , Brasil, R. M. L. R. F , Fenili, A. , Belato, D. , and Felix, J. L. P , 2003, "An overview on non-ideal vibrations," Meccanica 30 (5), 613-621 .

Balthazar, J. M. , Mook, D. T. , Webei; H. I. , Brasil, R. M. L. R. F , Fenili, A. , Belato, D. , and Felix, J. L. P , 2001, "Recent results on vibrating problems with limited power supply," in Proceedings of the 6th Conference on Dynamical Systems Theory and Applications, Lodz, Poland, December 10-12, pp. 27-50 .

Blekhman, I. I. , 1988, Self-Synchvnization in Science and Technology, ASME Press, NY

Blekhman, I. I. , 2000, Vibrational Mechanics: Nonlinear Dynamic Eftects, General Approach, Applications, World Scientific, Singapore .

Brasil, R. M. L. R. F. , 1999, "Multiple scales analysis of nonlinear oscillations of a portal frame foundation for several machines,' Journal of the BraZilian Society of Mechanical Sciences 21 (4), 641-654 .

Dimentberg, M. , Cobb, E. , and Mensching, J. , 2001, "Self-synchronization of transient rotations in multiple shaft systems," Journal of Vibration and Control 7, 221-232 .

Kang, Y. , Chao, C. P , Chou, C. C. , Chu, M. H. , and Mu, L. H. , 2002, "An integration method for detecting chaotic responses of nonlinear systems subjected to double excitations," International Journal of Non-Linear Mechanics 37, 1073-1077 .

Kononenko, V , 1969, Vibrating Systems with Limited Power Supply, Illife, London .

Nayseh, A. H. and Mock, D. T , 1979, Nonlinear Oscillation, Wiley-Interscience, NY

10.

Nóbrega, P G. B., 1994, "Auto-sincronizaqao de motores nao-ideais apoiados em estruturas elasticas," Dissertavao de Mestrado, EP, Universidade de Sao Paulo.

11.

Palacios, J. L., 2002, "Teoria de sistemas vibratórios não-lineares e não-ideals," Tese de Doutorado (in Portuguese), Universidade Estadual de Campinas, Campinas, SP, Brasil, 181 pp.

12.

Palacios, J. L. , Balthazar; J. M. , and Brasil, R. M. L. R. F. , 2003, "On the non-linear dynamics of a non-linear system under two non-ideals excitations," in Proceedings of the X DINAME, Ubatuba, SP, Brazil, March 10-14, pp. 381--386 .

13.

Palacios, J. L. , Balthazar, J. M. , and Brasil, R. M. L. R. F. , 2003, "A short note on the non-linear dynamics of a non-linear system under two non-ideals excitations," Journal of the Brazilian Society of Mechanical Sciences, vol 25, 4 pp. 39-395 .

14.

Sommerfeld, A., 1904, "Beitrdge zum dynarnischen ausbau der festigkeitslehe," Physikal Zeitschrift 3, 266-286.