Nonlinear Behavior of a Suspended Particle in  Single-Axis Acoustic Levitators

Celso Abud; Mirosmar  Rodrigues; Tiago Ramos

doi:10.31686/ijier.vol7.iss12.2016

Authors

Celso Abud Federal University of Goiás - UFG, Goiás, Brazil.
Mirosmar Rodrigues Federal University of Goiás - UFG, Goiás, Brazil
Tiago Ramos University of São Paulo - USP, São Paulo, Brazil

DOI:

https://doi.org/10.31686/ijier.vol7.iss12.2016

Keywords:

Nonlinear Phenomena, Acoustic Levitation, Lyapunov Exponents

Abstract

The nonlinear behavior of a suspended sphere in a single-axis acoustic levitator was studied. Spontaneous oscillations of the sphere in this levitator were experimentally analyzed recording its positions using a high speed camera. A mathematical model based on acoustic radiation forces and real parameters is proposed to describe the dynamics of the sphere movement and its stability. The stability of the motion was investigated via a Lyapunov exponent diagram. We observed that the axial and radial movements of small spheres under levitation may present regular stability and chaotic ones. The Lyapunov exponent diagram for the model shows a complexity structure sharing different regions of stability according to the model parameters.

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Author Biographies

Celso Abud, Federal University of Goiás - UFG, Goiás, Brazil.

Institute of Mathematics and Technology.
Mirosmar Rodrigues, Federal University of Goiás - UFG, Goiás, Brazil

Department of Mining Engineering,
Tiago Ramos, University of São Paulo - USP, São Paulo, Brazil

Department of Mechatronics and Mechanical Systems Engineering,

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