Nonlinear Response of Fluid-Filled Membrane in Gravity Waves
Publication: Journal of Engineering Mechanics
Volume 129, Issue 7
Abstract
This paper describes a time-domain model for the nonlinear response of fluid-filled membranes in gravity waves. A formulation based on the principle of virtual work provides an integral governing equation for membrane deformation that fully accounts for geometric nonlinearity, which is known to be important even for relatively small deformation. The incident wave amplitude and membrane deformation are considered to be small, to allow linearization of the hydrodynamic problems. The potential flows inside and outside the membrane are solved by two boundary element models, which are coupled to the finite element model of the membrane. An iterative scheme based on Newmark’s method integrates the resulting nonlinear equations of motion in time. The computed results for a bottom-mounted fluid-membrane system show favorable agreement with available experimental and numerical data. Membrane geometric nonlinearity increases the system stiffness due to strain-stiffening and gives rise to hysteresis response at some frequencies.
Get full access to this article
View all available purchase options and get full access to this article.
References
Bhattacharyya, R. (1978). Dynamics of marine vehicles, Wiley-Interscience, New York, 498.
Broderick, L. L., and Jenkins, C. H.(1993). “Experimental investigation of fluid-filled membrane breakwaters.” J. Waterw., Port, Coastal, Ocean Eng., 119(6), 639–656.
Broderick, L. L., and Leonard, J. W.(1992). “Nonlinear water-wave structure interaction.” Comput. Struct., 44(4), 837–842.
Broderick, L. L., and Leonard, J. W.(1995). “Nonlinear response of membranes to ocean waves using boundary and finite elements.” Ocean Eng., 22(7), 731–745.
Clément, A.(1996). “Coupling of absorbing boundary conditions.” J. Comput. Phys., 126, 139–151.
Cook, R. D., Malcus, D. S., and Plesha, M. E. (1989). Concepts and applications of finite element analysis, Wiley, New York, 630.
Han, P. S. (1986). “Interactive Non-linear Analysis of Wind-Loaded Pneumatic Membrane Structure.” PhD dissertation, University of British Columbia, Vancouver, Canada.
Isaacson, M., and Cheung, K. F.(1991). “Second order wave diffraction around two-dimensional bodies by time domain-method.” Appl. Ocean. Res., 13(4), 175–186.
Israeli, M., and Orszag, S. A.(1981). “Approximation of radiation boundary conditions.” J. Comput. Phys., 41, 115–135.
Leonard, J. W. (1988). Tension structures-behavior and analysis, McGraw-Hill, New York, 400.
Ohyama, T., Tanaka, M., Kiyokawa, T., Uda, T., and Murai, Y.(1989). “Transmission and reflection characteristics of waves over a submerged flexible mound.” Coastal Eng. Japan, 32(1), 53–68.
Phadke, A. C. (2001). “Hydrodynamics of Fluid-Filled Membrane in Gravity Waves.” PhD dissertation, University of Hawaii, Honolulu, Hawaii.
Phadke, A. C., and Cheung, K. F.(1999). “Response of bottom-mounted fluid-filled membrane in gravity waves.” J. Waterw., Port, Coastal, Ocean Eng., 125(6), 294–303.
Phadke, A. C., and Cheung, K. F.(2001). “Resonance and response of fluid-filled membrane in gravity waves.” Appl. Ocean. Res., 23(1), 15–27.
Stoker, J. J. (1950). Nonlinear vibrations in mechanical and electrical systems, Interscience, New York, 273.
Uemura, M. (1972). “Membrane tension and deformation in cylindrical pneumatic structures subject to wind loads.” Proc., Pacific Symposium on Tension Structures and Space Frames, International Association for Shell and Space Structures, Tokyo, 2, 199–210.
Zhao, R.(1995). “A complete linear theory for a two-dimensional floating and liquid-filled membrane structure in waves.” J. Fluids Struct., 9(8), 937–947.
Zhao, R., and Aarsnes, J. V.(1998). “Numerical and experimental studies of a floating liquid-filled membrane structure in waves.” Ocean Eng., 25(9), 753–765.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 129 • Issue 7 • July 2003
Pages: 739 - 750
Copyright
Copyright © 2003 American Society of Civil Engineers.
History
Received: Jul 16, 2001
Accepted: Aug 1, 2002
Published online: Jun 13, 2003
Published in print: Jul 2003
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.