Subharmonic generation, chaos, and subharmonic resurrection in an acoustically driven fluidfilled cavity
Abstract
Traveling wave solutions of the nonlinear acoustic wave equation are obtained for the fundamental and second harmonic resonances of a fluidfilled cavity. The solutions lead to the development of a nonautonomous toy model for cavity oscillations. Application of the Melnikov method to the model equation predicts homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos. The threshold value of the drive displacement amplitude at tangency is obtained in terms of the acoustic drive frequency and fluid attenuation coefficient. The model prediction of subharmonic generation leading to chaos is validated from acoustooptic diffraction measurements in a waterfilled cavity using a 5 MHz acoustic drive frequency and from the measured frequency spectrum in the bifurcation cascade regime. The calculated resonant threshold amplitude of 0.2 nm for tangency is consistent with values estimated for the experimental setup. Experimental evidence for the appearance of a stable subharmonic beyond chaos is reported.
 Authors:
 NASA Langley Research Center, Research Directorate, Hampton, Virginia 23681 (United States)
 Adler Consultants, Inc./Ohio State University, Columbus, Ohio 43210 (United States)
 Publication Date:
 OSTI Identifier:
 22405044
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; ATTENUATION; BIFURCATION; CHAOS THEORY; DIFFRACTION; FLUIDS; HARMONIC GENERATION; MATHEMATICAL SOLUTIONS; MHZ RANGE; NONLINEAR PROBLEMS; RESONANCE; SOUND WAVES; TRAVELLING WAVES; WATER; WAVE EQUATIONS
Citation Formats
Cantrell, John H., Email: john.h.cantrell@nasa.gov, Yost, William T., and Adler, Laszlo. Subharmonic generation, chaos, and subharmonic resurrection in an acoustically driven fluidfilled cavity. United States: N. p., 2015.
Web. doi:10.1063/1.4913521.
Cantrell, John H., Email: john.h.cantrell@nasa.gov, Yost, William T., & Adler, Laszlo. Subharmonic generation, chaos, and subharmonic resurrection in an acoustically driven fluidfilled cavity. United States. doi:10.1063/1.4913521.
Cantrell, John H., Email: john.h.cantrell@nasa.gov, Yost, William T., and Adler, Laszlo. 2015.
"Subharmonic generation, chaos, and subharmonic resurrection in an acoustically driven fluidfilled cavity". United States.
doi:10.1063/1.4913521.
@article{osti_22405044,
title = {Subharmonic generation, chaos, and subharmonic resurrection in an acoustically driven fluidfilled cavity},
author = {Cantrell, John H., Email: john.h.cantrell@nasa.gov and Yost, William T. and Adler, Laszlo},
abstractNote = {Traveling wave solutions of the nonlinear acoustic wave equation are obtained for the fundamental and second harmonic resonances of a fluidfilled cavity. The solutions lead to the development of a nonautonomous toy model for cavity oscillations. Application of the Melnikov method to the model equation predicts homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos. The threshold value of the drive displacement amplitude at tangency is obtained in terms of the acoustic drive frequency and fluid attenuation coefficient. The model prediction of subharmonic generation leading to chaos is validated from acoustooptic diffraction measurements in a waterfilled cavity using a 5 MHz acoustic drive frequency and from the measured frequency spectrum in the bifurcation cascade regime. The calculated resonant threshold amplitude of 0.2 nm for tangency is consistent with values estimated for the experimental setup. Experimental evidence for the appearance of a stable subharmonic beyond chaos is reported.},
doi = {10.1063/1.4913521},
journal = {Chaos (Woodbury, N. Y.)},
number = 2,
volume = 25,
place = {United States},
year = 2015,
month = 2
}

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