Chaotic vibration of an autoparametrical system with the spherical pendulum

• Autorzy: Sado D. , Freundlich J. , Bobrowska A.

Identyfikatory

DOI

10.15632/jtam-pl.55.3.779

• Języki publikacji: EN

Abstrakty

EN

In the paper, the dynamics of a three degree of freedom vibratory system with a spherical pendulum in the neighbourhood of internal and external resonance is considered. It has been assumed that the spherical pendulum is suspended to the main body which is then suspended to the element characterized by some elasticity and damping. The system is excited harmonically in the vertical direction. The equation of motion has been solved numerically. The influence of initial conditions on the behaviour of the spherical pendulum is investigated. In this type of the system, one mode of vibration may excite or damp another one, and for different kinds of periodic vibrations there may also appear chaotic vibrations. For characterization of an irregular chaotic response, time histories, bifurcation diagrams, power spectral densities, Poincar´e maps and the maximum Lyapunov exponents have been calculated.

Słowa kluczowe

EN

spherical pendulum; energy transfer; coupled oscillators; chaos

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2017
• Tom: Vol. 55 nr 3
• Strony: 779--786
• Opis fizyczny: Bibliogr. 7 poz., rys.

Twórcy

autor

Sado D.

• Warsaw University of Technology, Institute of Machine Design Fundamentals, Warsaw, Poland

autor

Freundlich J.

• Warsaw University of Technology, Institute of Machine Design Fundamentals, Warsaw, Poland

autor

Bobrowska A.

• Warsaw University of Technology, Institute of Machine Design Fundamentals, Warsaw, Poland

Bibliografia

• 1. Leung A.Y.T., Kuang J.L., 2006, On the chaotic dynamics of a spherical pendulum with a harmonically vibrating suspension, Nonlinear Dynamics, 43, 213-238
• 2. Miles J.W., Zou Q.P., 1993, Parametric excitation of a detuned spherical pendulum, Journal of Sound and Vibration, 164, 2, 237-250
• 3. Mitrov R., Grigorov B., 2009, Dynamic behaviour of a spherical pendulum with spatially moving pivot, Zeszyty Naukowe Politechniki Poznańskiej, 9, 81-91
• 4. Naprstek J., Fischer C., 2009, Auto-parametric semi-trival and post-critical response of a spherical pendulum damper, Computers and Structures, 87, 1204-1215
• 5. Sado D., 2010, Regular and Chaotic Vibration in Selected Pendulum Systems (in Polish), WNT, Warsaw
• 6. Viet L.D., 2015, Partial stochastic linearization of a spherical pendulum with Coriolis damping produced by radial spring and damper, Journal Vibration and Acoustics, 137, 5, 1-9, DOI: 10.1115/1.4030663
• 7. Witkowski B., Perlikowski P., Prasad A., Kapitaniak T., 2014, The dynamics of co- and counter rotating coupled spherical pendula, The European Physical Journal Special Topics, 223, 4, 707-720

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)