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- Title
DYNAMICS OF ELASTIC SHEETS WITH BENDING STIFFNESS.
- Authors
HILGERS, M. G.
- 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.
- Subjects
STRAIN energy; STIFFNESS (Mechanics); DEFORMATIONS (Mechanics); STRAINS &; stresses (Mechanics); HAMILTON'S equations; ELASTIC solids; KINETIC energy; DYNAMICS
- Publication
Quarterly Journal of Mechanics & Applied Mathematics, 1997, Vol 50, Issue 4, p525
- ISSN
0033-5614
- Publication type
Article
- DOI
10.1093/qjmam/50.4.525