Superresonant systems of scatterers. II

Abstract

S y s t e m s of identical monopole scatterers interacting through multiple scatter will, under certain conditions, develop normal modes, i.e., bonafide resonant behavior at certain frequencies (corresponding to poles of the multiple scatter coefficients). This occurs when the monopole scattering cross sections are large enough to give significant interaction; this happens for highly tuned scatterers, e.g., gas-filled bubbles/balloons/shells in water, insonified at frequencies near their characteristic resonant frequencies. This phenomenon has been called superresonance (SR) and has been discussed mostly in the case when the primary energy transport mechanism between scatterers is a cylindrically spreading boundary wave, like the flexure mode of a thin elastic plate [I. Tolstoy, J. Acoust. Soc. Am. 80, 282–294 (1986)]. The singularity of the field at the scatterer is removed by introducing the finite radius of the scatterers. The present article investigates the effect of the plate material on the SR phenomenon, showing that for a steel plate and a pair of bubbles/balloons (doublet) the acoustic amplitudes on the scatterer surfaces may be 3×103 times the free-field value, i.e., one has an amplitude amplification factor μ≊3×103, where μ decreases as the plate rigidity decreases. On the other hand, in a homogeneous acoustic full space SR does not, strictly speaking, occur: The scatterer system does not become fully resonant (the theory does not indicate the existence of poles) since spherically spreading acoustic modes are less efficient transporters of energy between scatterers than the cylindrically spreading boundary modes. Nevertheless, simple symmetrical systems of bubbles/balloons/shells can still demonstrate a tendency to resonate, i.e., produce sharp peaks on the μ curve. Plane and polyhedral configurations may still yield μ≊102 at each scatterer. To distinguish this from bonafide SRs near a plate, we call these quasiresonances (QRs). It is shown, however, that partial shielding between selected pairs of scatterers in such configurations affects the phase relationships in the system in such a way as to allow the appearance of true SRs.