Abstract
A theory describing the motion of nonlinear elastic membranes with bending stiffness is formulated. The strain energy density for these materials depends on the second derivatives of the deformation as well as the first derivatives. A compatible kinetic energy density requires velocity gradient terms to agree to the same order as the strain energy density. The equations of motion are derived using Hamilton's principle. Due to the velocity gradient dependence of the kinetic energy density, the equations of motion are found to possess a rotary inertia term which is considered from a variety of perspectives. The motion of a spinning inflated tube is determined.
Recommended Citation
Hilgers, M. G. (1997). Dynamics of Elastic Sheets with Bending Stiffness. Quarterly Journal of Mechanics and Applied Mathematics, 50(4), pp. 517-543. Oxford University Press.
The definitive version is available at https://doi.org/10.1093/qjmam/50.4.525
Department(s)
Business and Information Technology
International Standard Serial Number (ISSN)
0033-5614
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Oxford University Press, All rights reserved.
Publication Date
01 Jan 1997
