Subharmonic generation, chaos, and subharmonic resurrection in an acoustically driven fluid-filled cavity.
Traveling wave solutions of the nonlinear acoustic wave equation are obtained for the fundamental and second harmonic resonances of a fluid-filled cavity. The solutions lead to the development of a non-autonomous 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 acousto-optic diffraction measurements in a water-filled 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 set-up. Experimental evidence for the appearance of a stable subharmonic beyond chaos is reported.
NASA Langley Research Center, Research Directorate, Hampton, Virginia 23681, USA.
John H
JH
Cantrell
Adler Consultants, Inc./Ohio State University, Columbus, Ohio 43210, USA.
Laszlo
L
Adler
NASA Langley Research Center, Research Directorate, Hampton, Virginia 23681, USA.
William T
WT
Yost