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.
Dynamics of a Hyperelastic Gas-Filled Spherical Shell in a Viscous Fluid
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the Applied Mechanics Division, Sept. 16, 2002; final revision, July 23, 2003. Associate Editor: R. C. Benson. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Journal of Applied Mechanics, Department of Mechanical and Environmental Engineering, University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication in the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Allen, J. S., and Rashid, M. M. (May 5, 2004). "Dynamics of a Hyperelastic Gas-Filled Spherical Shell in a Viscous Fluid ." ASME. J. Appl. Mech. March 2004; 71(2): 195–200. https://doi.org/10.1115/1.1653722
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