In this paper we propose a mathematical model with
tensorial analysis for a single cavitating microshell bubble
immersed in a newtonian liquid, excited by an ultrasound field.
We obtain a system of nonlinear differential equations
Rayleigh-Plesset kind for a thin shell working as a Mooney
Rivlin hyperelastic solid. Numerical solutions of the full
equation are obtained, for periodic and nonperiodic oscillations,
for different values of the elastic parameters. We also present a
frequency analysis for the nonlinear behaviour of the system by
obtaining an analytical solution with the method of Multiple
Scale Analysis. All of these is carried out taking into account
the values of the parameters used in the Contrast Agents
Papers presented to the 12th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Costa de Sol, Spain on 11-13 July 2016.