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Published May 2016 | Published + Submitted
Journal Article Open

Nonlinear vibrational-state excitation and piezoelectric energy conversion in harmonically driven granular chains


This article explores the excitation of different vibrational states in a spatially extended dynamical system through theory and experiment. As a prototypical example, we consider a one-dimensional packing of spherical particles (a so-called granular chain) that is subject to harmonic boundary excitation. The combination of the multimodal nature of the system and the strong coupling between the particles due to the nonlinear Hertzian contact force leads to broad regions in frequency where different vibrational states are possible. In certain parametric regions, we demonstrate that the nonlinear Schrödinger equation predicts the corresponding modes fairly well. The electromechanical model we apply predicts accurately the conversion from the obtained mechanical energy to the electrical energy observed in experiments.

Additional Information

© 2016 American Physical Society. Received 10 October 2015; revised manuscript received 22 March 2016; published 5 May 2016. C.C. was partially supported by the ETH Zurich Foundation through Seed Project ESC-A 06-14. E.G.C., C.D., and P.G.K. acknowledge support from the U.S. AFOSR under Grant No. FA9550-12-10332. P.G.K. also acknowledges support from the NSF under Grant No. DMS-1312856, from the ERC and FP7-People under Grant No. 605096, and from the Binational (U.S.-Israel) Science Foundation through Grant No. 2010239. P.G.K.'s work at Los Alamos was supported in part by the U.S. Department of Energy. J.Y. is grateful for the support of the NSF (CMMI-1414748), the U.S. ONR (N000141410388), and the ADD of Korea (UD140059JD). J.Y. and P.G.K. also acknowledge support from the ARO (W911NF-15-1-0604).

Attached Files

Published - PhysRevE.93.052203.pdf

Submitted - 1510.04753.pdf


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