Abstract
In this work, we studied numerically, analytically and experimentally the nonlinear dynamics of this system, in particular, harmonic generation and the balance between nonlinearity and dispersion. In the experimental setup, each magnet is attached to a T shaped rod with length L and the system presents a very lowdamping. Three regimes have been explored exciting the chain, forcing the first pendulum with an harmonic force of long wavelength with respect to a and with such amplitude that the dispersion relation still remains valid. We have studied harmonic generation when; (a) the frequencies of the Firs t harmonic (driven force) and the second harmonic generated by the nonlinearity lies into the non-dispersive part of the dispersion relation (almost linear). In this case the second harmonic starts to increase while first harmonic decreases. (b) The driven frequency is in the non-dispersive part of the dispersion relation but the second harmonic is evanescent. The amplitude of the second harmonic reaches a constant value along the chain. (c) The frequency of the second harmonic lies in the dispersive part of the dispersion relation. Harmonic components travel with different velocities and beating appears. Analytical results and numerical simulations are in good agreement with the experimental results.
BibTeX citation
@inproceedings{MehremNoLineal2016,
author = {A. Mehrem and N. Jiménez and L. J Salmerón-Contreras and X. García-Andrés and R. Picó and L. M. García-Raffi and V. J.Sánchez-Morcillo},
booktitle = {No Lineal 2016: International conference on nonlinear mathematics and physics. Seville, Spain. 7 - 10 June},
editor = {Book of abstracts},
month = {6},
organization = {Universidad de Sevilla},
pages = {75},
series = {Oral},
title = {Second harmonic generation in a chain of magnetic pendulums},
url = {http://congreso.us.es/nolineal16},
year = {2016}
}