Propagation of acoustic wave in viscoelastic medium permeated with air bubbles

Based on the modification of the radial pulsation equationof an individual bubble, an effective medium method (EMM) is presented forstudying propagation of linear and nonlinear longitudinal acoustic wavesin viscoelastic medium permeated with air bubbles. A classical theorydeveloped previously by Gaunaurd (Gaunaurd GC and "{U}berall H, {em J.Acoust. Soc. Am}., 1978; 63: 1699--1711) is employed to verify the EMM under linear approximationby comparing the dynamic (i.e. frequency-dependent) effective parameters,and an excellent agreement is obtained. The propagation of longitudinalwaves is hereby studied in detail. The results illustrate that the nonlinearpulsation of bubbles serves as the source of second harmonic wave and thesound energy has the tendency to be transferred to second harmonic wave.Therefore the sound attenuation and acoustic nonlinearity of theviscoelastic matrix are remarkably enhanced due to the system's resonanceinduced by the existence of bubbles.