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IMA Journal of Applied Mathematics Advance Access originally published online on December 5, 2008
IMA Journal of Applied Mathematics 2009 74(1):20-34; doi:10.1093/imamat/hxn039
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© The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Analysis of the Rayleigh–Plesset equation with chirp excitation

Euan Barlow{dagger} and Anthony J. Mulholland

Department of Mathematics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK

Anthony Gachagan

Department of Electronic and Electrical Engineering, The Centre for Ultrasonic Engineering, University of Strathclyde, 204 George Street, Glasgow G1 1XW, UK

Alison Nordon and Kenneth MacPherson

WestCHEM, Department of Pure and Applied Chemistry, Centre for Process Analytics and Control Technology, University of Strathclyde, 295 Cathedral Street, Glasgow G1 1XL, UK

{dagger} Email: rs.ebar{at}maths.strath.ac.uk

Received on June 27, 2007; Revision received March 19, 2008. Accepted on October 24, 2008

The case of a bubble being insonified by an ultrasonic excitation in the form of a linear chirp is considered here. The dynamical equation of the bubble's motion is solved analytically and compared to a numerical solution. The analytical solution is then used to investigate the problem of maximizing the amplitude of the second harmonic with respect to the various system and signal parameters.

Keywords: chirp; Rayleigh–Plesset; bubble.


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