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Nonlinearity brings a whole range of
phenomena that are not found in linear systems. In single-degree-of-freedom
systems, these include multiple solutions and jumps; limit cycles; frequency
entrainment; natural-frequency shifts; subharmonic, superharmonic,
combination, and ultrasubharmonic resonances; period-multiplying and
demultiplying bifurcations; and chaos. For multidegree-of-freedom and
continuous systems, another nonlinear phenomenon is an interaction and
energy exchange among different modes. This energy exchange can be dangerous
for typically energy is transferred from the low-amplitude high-frequency
components of the motion associated with the high modes to the
high-amplitude low-frequency components associated with the low modes. Thus,
the modal interaction makes it possible for a high-frequency low-amplitude
excitation, which is capable of doing a lot of work on the system in a short
period, to produce a large-amplitude low-frequency response. In addition, it
has been found that, in weakly nonlinear systems where there exists a
special relationship between two or more natural frequencies and an
excitation frequency, the long-time response can contain large contributions
from many linear modes. Modal interactions can lead to dangerously large
responses in the very modes that are insignificant according to linear
analysis. Consequently, the use of classical transfer functions and modal
analysis identification techniques is inappropriate and may lead to
erroneous conclusions. Some of these phenomena are illustrated using
examples drawn from ship motion, structures, flutter, cranes mounted on
ships, identification, and control.
Dr. Ali H. Nayfeh is University
Distinguished Professor of Engineering at Virginia Polytechnic Institute and
State University. Dr. Nayfeh was born in Jordan and received a B.S. degree
in Engineering Science, and M.S. and Ph.D. degrees in Aeronautics and
Astronautics all from Stanford. He is
the author of more than 359 papers in refereed journals, and 10 books. He
has supervised 59 Ph.D. dissertations. He is the Editor of the Wiley
Book Series on Nonlinear Science and the Editor-in-Chief of Nonlinear
Dynamics and Journal of Vibration and Control. He is a fellow of
APS, AIAA, ASME, and the American Academy of Mechanics. His other awards
include the Kuwait Prize in Basic Sciences, an
Alexander von Humboldt Foundation
Award, the AIAA Pendray Aerospace Literature Award, the ASME Den
Hartog Award, Honorary Doctorates from St. Petersburg University, Russia,
and the Technical University of Munchen, Germany, and the Frank J. Maher
Award for Excellence in Engineering Education. He established and served as
Dean of the College of Engineering, Yarmouk University, Jordan from
1980-1984. |
