The dynamical response of a gas-filled, spherical elastic shell immersed in a viscous fluid is of interest in a number of different scientific and technological contexts. In this article, this problem is formulated and studied numerically, within a purely mechanical setting. For spherically symmetric motions, a neo-Hookean shell material, and an incompressible surrounding fluid, the equation of motion can be obtained through an integration in the radial coordinate. The resulting nonlinear initial-value problem must be integrated numerically. An interesting feature of the system response is the possibility of a departure from bounded oscillation for large-amplitude far-field forcing. The amplitude at which this departure occurs is found to be highly dependent on the forcing frequency. A stability map in the forcing frequency/amplitude plane is an important result of this study.

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