Free Vibrations of an Elastically Supported Geometrically Nonlinear Column Subjected to a Generalized Load with a Force Directed toward the Positive Pole
Publication: Journal of Engineering Mechanics
Volume 137, Issue 11
Abstract
The formulation of and solution to the problem of the free vibrations of a geometrically nonlinear column, supported at the loaded end by a spring with linear characteristics, are discussed in the paper. Transversal free vibrations around a rectilinear form of static equilibrium are considered in this work. The considered system was subjected to a generalized load with a force directed toward the positive pole. The boundary problem was formulated using Hamilton’s principle and the straightforward expansion method. A series of numerical simulations were conducted using the mathematical model. The characteristic curve in the plane of load versus natural frequency was assigned to different parameters of the considered system. Experimental research was carried out to confirm the accuracy of the assumed mathematical model. The research relied on modal analysis and the determination of the natural frequency of the system for chosen values of an external load.
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Acknowledgments
The study has been carried out within research project No. UNSPECIFIEDN N501 117236 awarded by the Ministry of Science and Higher Education and projects No. UNSPECIFIEDBW-1-101-207/03/P and UNSPECIFIEDBS-1-101-302-99/P of the Czestochowa University of Technology.
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Published In
Journal of Engineering Mechanics
Volume 137 • Issue 11 • November 2011
Pages: 740 - 748
Copyright
© 2011 American Society of Civil Engineers.
History
Received: May 10, 2010
Accepted: Jun 13, 2011
Published online: Jun 17, 2011
Published in print: Nov 1, 2011
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