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.
Department of Mechanical and Process Engineering (D-MAVT), Swiss Federal Institute of Technology (ETH), 8092 Zürich, Switzerland.|Department of Mathematics, Bowdoin College, Brunswick, Maine 04011, USA.
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Chong
Aeronautics & Astronautics, University of Washington, Seattle, Washington 98195-2400, USA.|Division of Mechanical System Engineering, Automotive Hi-Technology Research Center, Chonbuk National University, 567 Baeje-daero, deokjin-gu, Jeonju-si, Jeollabuk-do,54896, Republic of Korea.
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Kim
Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
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Charalampidis
Aeronautics & Astronautics, University of Washington, Seattle, Washington 98195-2400, USA.
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Kim
Aeronautics & Astronautics, University of Washington, Seattle, Washington 98195-2400, USA.
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Li
Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
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Kevrekidis
Department of Mechanical and Process Engineering (D-MAVT), Swiss Federal Institute of Technology (ETH), 8092 Zürich, Switzerland.
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Lydon
Department of Mechanical and Process Engineering (D-MAVT), Swiss Federal Institute of Technology (ETH), 8092 Zürich, Switzerland.|Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA.
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Daraio
Aeronautics & Astronautics, University of Washington, Seattle, Washington 98195-2400, USA.
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Yang