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Non‐linear flexings in a periodically forced floating beam
Author(s) -
Lazer A. C.,
McKenna P. J.
Publication year - 1991
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670140102
Subject(s) - mathematics , forcing (mathematics) , beam (structure) , amplitude , cusp (singularity) , mathematical analysis , range (aeronautics) , boundary (topology) , boundary value problem , periodic boundary conditions , geometry , physics , optics , materials science , composite material
This paper considers periodic flexing in a floating beam, in the presence of a small periodic forcing term. The beam is considered as a vibrating beam with the free‐end boundary condition, in the presence of an additional restoring force due to flotation, which becomes zero as soon as the beam lifts out of the water. The equation is therefore non‐linear. A theorem is proved which shows that in the presence of small periodic forcing terms, both small‐ and large‐amplitude solutions can exist. Numerical evidence is presented, which shows that the large‐amplitude solutions are stable over a wide range of frequency and amplitude, and suggests a cusp‐like surface for the multiple solutions.