Abstract
Systems of identical precisely spaced bubbles or similar monopole scatterers in water-e.g., inflated balloons or thin-walled shells-insonified at frequencies <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{SR}</tex> dose to their fundamental radial resonance <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{0}</tex> (bubble) frequency may themselves display resonance modes or superresonances (SR's) [1]. Ordinary single-bubble resonances magnify the local free-field pressure amplitude <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p_{1}</tex> by a factor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(ka)^{-1}</tex> , <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</tex> being the radius and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> the wavenumber in water: for air bubbles or balloons in water, this factor is of the order of 70. Under SR conditions each member of the system amplifies the local free-field amplitude by a further factor of order <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(ka)^{-1}</tex> . Depending upon geometry and other constraints, the pressure field <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_{SR}</tex> on the surface and in the interior of each scatterer will then be in the range of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10^{3}p_{1}</tex> to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5 \times 10^{3} p_{1}</tex> . This paper investigates the sensitivity of this phenomenon to small departures from the ideal model. In particular, it examines the effect of small differences in scatter positioning and volumes in the context of an SR system consisting of two bubbles/balloons close to the boundary of a thin elastic plate overlying a fluid half-space. It is found that, to observe the SR phenomenon, radii and positions should be controlled to within approximately 1/2 percent. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_{SR}</tex> is also sensitive to the angle of incidence of the plane wave train. For the simple system examined here, this sensitivity is considerable for either flexural wave trains or volume acoustic waves incident upon the bubble/ balloon pair (doublet). Practical uses of the phenomenon may range from the design of passive high- <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> acoustical filter/amplifiers and acoustical lenses to improved source efficiencies.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
