Frequency response curves for a Mooney-Rivlin hyperelastic microbubble oscillating as a contrast agent in an acoustic pressure field.

In this work, we have developed numerical simulations and weakly nonlinear analysis based on the multiple-scales perturbation technique for a coated microbubble that performs radial pulsations subject to an acoustic pressure disturbance in the far-field and whose encapsulated hyperelastic material obeys the Mooney-Rivlin equation. Departing from an elastic coating as a hyperelastic shell of finite thickness, we assume eventually that the shell is of very small thickness in comparison with the microbubble radius. Under this condition, we then perform weakly nonlinear analysis, to identify resonance conditions for small pressure disturbances of the acoustic field. In parallel and also for the limit of small thickness, we have carried out numerical simulations of the radial motion of the microbubble, identifying the onset of limit cycles via the construction of Poincare maps. Under both schemes, we have recognized the importance of two dimensionless hyperelastic parameters that dictate the main behavior of the oscillations: α

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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.