Nonlinear Random Vibrations of Beams with In-Span Supports via Statistical Linearization with Constrained Modes
Publication: Journal of Engineering Mechanics
Volume 145, Issue 6
Abstract
A statistical linearization technique is developed for determining second-order response statistics of beams with in-span elastic concentrated supports. The nonlinearities considered relate both to the support restoring forces, and to the assumption of relatively large beam displacements. A significant novel aspect of the technique is the utilization of constrained modes involving generalized functions in their definition; thus, shear-force discontinuities at the support locations can be readily accounted for. Overall, a set of nonlinear modal equations is derived and replaced by a set of equivalent linear ones based on an error minimization scheme in a mean square sense. This yields a set of algebraic nonlinear equations for the beam response second-order statistics, which can be readily solved in a computationally efficient manner via a simple iterative scheme. It is noted that the technique applies to an arbitrary number of supports yielding accurate and computationally efficient solutions for the second-order statistics of the response. Two illustrative numerical examples are considered for assessing the reliability and accuracy of the technique as compared with pertinent Monte Carlo simulation data. The latter are generated based on a boundary integral solution methodology in conjunction with a Newmark numerical integration scheme.
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Acknowledgments
This paper has been developed within the Marie Curie IRSES project “Large multipurpose platforms for exploiting renewable energy in open seas—PLENOSE” (Grant Agreement No. PIRSES-GA-2013-612581).
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Published In
Journal of Engineering Mechanics
Volume 145 • Issue 6 • June 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: May 22, 2018
Accepted: Oct 30, 2018
Published online: Apr 15, 2019
Published in print: Jun 1, 2019
Discussion open until: Sep 15, 2019
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