Analytical-numerical approach to analyze forced and parametric vibrations of some pendulum systems
Keywords:
pendulum systems; nonlinear normal vibrations; Rauscher method
Abstract
The parametric oscillations of physical pendulum and forced vibrations of a system with pendulum absorber are analyzed using the approach based on combined application of the concept of nonlinear normal vibration modes, the Rauscher method, and numerical procedures. Frequency responses are obtained.
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References
Lyapunov A. M. The general problem of the stability of motion. Princeton University Press, Princeton. – 1947.
Kauderer H. Nichtlineare Mechanik. Springer-Verlag, Berlin. – 1958.
Rosenberg R. Nonlinear vibrations of systems with many degrees of freedom // Advances of Applied Mechanics. – 1966. - Vol.9. - pp. 156–243.
Manevich L., Mikhlin Yu. Periodic solutions close to rectilinear normal vibration modes // Prikladnaja Matematica i Mekhanica (PMM USSR). – 1972. – v. 36. – рр. 1051–1058 (in Russian).
Manevich L., Mikhlin Yu., Pilipchuk V. The method of normal oscillation for essentially nonlinear systems. Nauka, Moscow. – 1989 (in Russian).
Avramov K., Mikhlin Yu. Nonlinear Dynamics of Elastic Systems // Models, Methods and Approaches. Scientific Centre “Regular and Chaotic Dynamics”. - Moscow-Izhevsk, 2010. – 704 p. (in Russian).
Mikhlin Yu., Avramov K. Nonlinear normal modes for vibrating mechanical systems // Review of theoretical developments. Applied Mechanics Review. – 2010. – v. 63. - pp. 4-20.
Rauscher M. Steady oscillations of system with nonlinear and unsymmetrical elasticity // Journal of Applied Mechanics. - 1938. - v. 5.
Yu. Mikhlin. Resonance modes of near-conservative nonlinear systems // Prikladnaja Matematica I Mekhanica (PMM USSR). – 1974. – v. 38. – pp. 425–429 (in Russian).
Kauderer H. Nichtlineare Mechanik. Springer-Verlag, Berlin. – 1958.
Rosenberg R. Nonlinear vibrations of systems with many degrees of freedom // Advances of Applied Mechanics. – 1966. - Vol.9. - pp. 156–243.
Manevich L., Mikhlin Yu. Periodic solutions close to rectilinear normal vibration modes // Prikladnaja Matematica i Mekhanica (PMM USSR). – 1972. – v. 36. – рр. 1051–1058 (in Russian).
Manevich L., Mikhlin Yu., Pilipchuk V. The method of normal oscillation for essentially nonlinear systems. Nauka, Moscow. – 1989 (in Russian).
Avramov K., Mikhlin Yu. Nonlinear Dynamics of Elastic Systems // Models, Methods and Approaches. Scientific Centre “Regular and Chaotic Dynamics”. - Moscow-Izhevsk, 2010. – 704 p. (in Russian).
Mikhlin Yu., Avramov K. Nonlinear normal modes for vibrating mechanical systems // Review of theoretical developments. Applied Mechanics Review. – 2010. – v. 63. - pp. 4-20.
Rauscher M. Steady oscillations of system with nonlinear and unsymmetrical elasticity // Journal of Applied Mechanics. - 1938. - v. 5.
Yu. Mikhlin. Resonance modes of near-conservative nonlinear systems // Prikladnaja Matematica I Mekhanica (PMM USSR). – 1974. – v. 38. – pp. 425–429 (in Russian).
Published
2014-03-11
How to Cite
KlimenkoА. А., & Mikhlin, Y. V. (2014). Analytical-numerical approach to analyze forced and parametric vibrations of some pendulum systems. Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control Systems», 25(1131), 118-125. Retrieved from https://periodicals.karazin.ua/mia/article/view/14236
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