Nonlinear waves in phononic rotational lattices

Abstract

We investigate the dynamics of mechanical waves propagating in a highly nonlinear one-dimensional lattice, consisting of rotating elements coupled by linear springs. The nonlinearity, of geometrical origin, is of cubic type. In the case of absence of pre-stress of the springs in the rest state, linear terms are absent and the system is purely nonlinear. An equation of motion for the chain is derived for a general geometry (for arbitrary spring-to-rotator length ratio), and its different limits are explored. As the system is highly nonlinear, it does not show linear dispersion at all, presenting what has been called an acoustic vacuum. Moreover, the obtained nonlinear dispersion is of optical type, i.e. the wavelength increases with the frequency of the wave. Analytical solutions for the amplitude of the fundamental wave and its third harmonic have been obtained in the rotating wave approximation. An experiment has been designed to check the main predictions of the theory. The system is excited at the boundary by driving harmonically the angle of the first rotator, and the motion of each rotator is tracked by video and processed to obtain the time evolution of the angles. Measurements show evidences of the nonlinear characteristics of the system, as the generation of harmonics or an amplitude-dependent transition from evanescent to propagating states, in agreement with the nonlinear dispersion characteristics obtained analytically. Other nonlinear features of this system are also illustrated.

@inproceedings{Sanchez-MorcilloGusevJimenez2016,
 author = {Víctor Sánchez-Morcillo and Vitalyi Gusev and Noé Jiménez},
 booktitle = {IMECE 2016: International Mechanical Engineering Congress \& Exposition, ASME. Phoenix, AZ, USA. November 15},
 editor = {Book of abstracts},
 month = {11},
 organization = {American Society of Mechanical Engineers},
 pages = {1},
 publisher = {ASME},
 series = {Oral},
 title = {Nonlinear waves in phononic rotational lattices},
 url = {www.asme.org/events/imece},
 year = {2016}
}