
Scientific paper ID 2121 : 2021/3
А PENDULUM SUSPENDED ON AN ELASTIC BEAM
Anastas Ivanov Ivanov The oscillations of a pendulum suspended on an elastic beam are examined.
The mathematical pendulum is a material point suspended on an ideal rigid and massless rod. The upper end of the rod is connected by a joint with an elastic beam on two supports. The beam is considered to be perfectly elastic and massless. The system has two degrees of freedom. The nonlinearity is due only to a geometric nature. A nonlinear system of two differential equations is derived. A numerical solution was made with the mathematical package MatLab. The laws of motion, generalized velocities, generalized accelerations, and phase trajectories are obtained. The internal force in the rod as a time function is also determined. The dynamical coefficient for the rod is calculated. In order to continue the task by preparing an actual model and conducting experimental research, the projections of the velocity and acceleration of the material point along the horizontal and vertical axes, as well as their magnitudes, are determined. The obtained results are presented graphically and analyzed in detail. The research has a theoretical and applied character. махало еластична греда геометрична нелинейност нелинейни трептения симулация MatLabpendulum elastic beam geometric nonlinearity nonlinear oscillations simulation MatLabAnastas Ivanov Ivanov BIBLIOGRAPHY [1] Palmieri P., A phenomenology of Galileo’s experiments with pendulums. British Society for the History of Science 2009, volume 42, issue 4, pp. 479513, doi: 10.1017/S0007087409990033. [2] Andriesse, C. D., Huygens: The Man Behind the Principle. Cambridge University Press, 2005, ISBN 9780521850902, p. 134. [3] William Tobin , The life and science of Léon Foucault: The man who proved the earth rotates. Cambridge University Press, 2003, ISBN 9780521808552, p. 272. [4] Amore P., Aranda A., Improved LinstedtPoincare method for the solution of nonlinear problems. J. Sound Vib., 283 (35), 2005, pp. 11151136. [5] Pisarev A.M., Mechanical vibrations. Tehnika, Sofia, 1985, p. 288, (in Bulgarian). [6] Cheshankov B.I., Theory of vibrations. TUSofia, 1992, p. 254, (in Bulgarian). [7] Ivanov A.I., Mathematical pendulum wrapped around a fixed cylinder. Proceedings of the annual university scientific conference of Vasil Levski National University, 2728 May 2021, Electronic edition, ISSN 23677481, pp. 21802189. [8] Djou P., Bozduganva V., Vitliemov V., Dynamics of a pendulum with variable length and dry friction, Jorn. “Mechanics of machines”, year XVII, book 3, 2009, ISSN 08619727, TUVarna, pp. 4144, (in Bulgarian). [9] Bozduganva V., Vitliemov V., Dynamics of pendulum with variable length and dry friction as a simulator of a swing, Jorn. “Mechanics of machines”, year XVII, book 3, 2009, ISSN 08619727, TUVarna, pp. 4548, (in Bulgarian). [10] Nikolov D. N., Marinov M. B., Ganev B. T., Djamijkov T. S., Nonintrusive Measurement of Elevator Velocity Based on Inertial and Barometric Sensors in Autonomous Node. Proceedings of the International Spring Seminar on Electronics Technology, 2020, doi: 10.1109/ISSE49702.2020.9121077. [11] Marinov M., Nikolov D., Ganev B., Nikolov G., Environmental noise monitoring and mapping. Proceedings of the International Spring Seminar on Electronics Technology, 2017, doi: 10.1109/ISSE.2017.8000992. [12] Ganev B., Nikolov D., Marinov M. B., Performance evaluation of MEMS pressure sensors. 11th National Conference with International Participation, ELECTRONICA 2020  Proceedings, 2020, doi: 10.1109/ELECTRONICA50406.2020.9305140. [13] Vitliemov V., Ivanov I., Robusttrajectory optimal synthesis of spread macroparticles. Jorn. “Mechanics of machines”, year XXII, book 2, 2014, ISSN 08619727, TUVarna, pp. 3 7, (in Bulgarian) 