%0 Journal Article %1 Schmitt1998 %A Schmitt, John M. %A Bayly, Philip V. %D 1998 %J Nonlinear Dynamics %K 70-05-experimental-work-for-problems-relating-to-mechanics-of-particles-and-systems 70k20-stability-for-nonlinear-problems-in-mechanics 70k40-forced-motions-for-nonlinear-problems-in-mechanics %N 1 %P 1--14 %R 10.1023/A:1008279910762 %T Bifurcations in the Mean Angle of a Horizontally Shaken Pendulum: Analysis and Experiment %U https://link.springer.com/article/10.1023%2FA%3A1008279910762 %V 15 %X A pendulum excited by high-frequency horizontal displacement of its pivot point will vibrate with small amplitude about a mean position. The mean value is zero for small excitation amplitudes, but if the excitation is large enough the mean angle can take on non-zero values. This behavior is analyzed using the method of multiple time scales. The change in the mean angle is shown to be the result of a pitchfork bifurcation, or a saddle-node bifurcation if the system is imperfect. Analytical predictions of the mean angle as a function of frequency and amplitude are confirmed by physical experiment and numerical simulation.

@article{Schmitt1998, abstract = {A pendulum excited by high-frequency horizontal displacement of its pivot point will vibrate with small amplitude about a mean position. The mean value is zero for small excitation amplitudes, but if the excitation is large enough the mean angle can take on non-zero values. This behavior is analyzed using the method of multiple time scales. The change in the mean angle is shown to be the result of a pitchfork bifurcation, or a saddle-node bifurcation if the system is imperfect. Analytical predictions of the mean angle as a function of frequency and amplitude are confirmed by physical experiment and numerical simulation.}, added-at = {2021-11-17T05:57:31.000+0100}, author = {Schmitt, John M. and Bayly, Philip V.}, biburl = {https://www.bibsonomy.org/bibtex/2d51506238c690b8c5a5c8fced64506c3/gdmcbain}, day = 01, doi = {10.1023/A:1008279910762}, interhash = {371c08fd05410d7a187eee2bda1e2ac3}, intrahash = {d51506238c690b8c5a5c8fced64506c3}, issn = {1573-269X}, journal = {Nonlinear Dynamics}, keywords = {70-05-experimental-work-for-problems-relating-to-mechanics-of-particles-and-systems 70k20-stability-for-nonlinear-problems-in-mechanics 70k40-forced-motions-for-nonlinear-problems-in-mechanics}, month = jan, number = 1, pages = {1--14}, timestamp = {2021-11-17T06:24:17.000+0100}, title = {Bifurcations in the Mean Angle of a Horizontally Shaken Pendulum: Analysis and Experiment}, url = {https://link.springer.com/article/10.1023%2FA%3A1008279910762}, volume = 15, year = 1998 }