Analytical Solution for an Infinite Euler-Bernoulli Beam on a Viscoelastic Foundation Subjected to Arbitrary Dynamic Loads
Publication: Journal of Engineering Mechanics
Volume 140, Issue 3
Abstract
An analytical solution for the dynamic response of an infinite beam resting on a viscoelastic foundation and subjected to arbitrary dynamic loads is developed in this paper. Fourier and Laplace transforms are utilized to simplify the governing equation of the beam to an algebraic equation, so that the solution can be conveniently obtained in the frequency domain. The convolution theorem is employed to convert the solution into the time domain. Final solutions of beam responses investigated are deflection, velocity, acceleration, bending moment, and shear force. The validation of the proposed solution is verified by considering the solutions of several special dynamic loads and comparing the degraded solution to the known results. Further complicated dynamic loads, such as impulsive loads and time-lag loads, are also discussed and analytical solutions are presented. These relationships can be an effective tool for practitioners.
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Acknowledgments
The research is mainly supported by the National Natural Science Foundation of China (Grant No. 51208296), the National Basic Research Program of China (973 Program No. 2011CB013600), and the China Postdoctoral Science Foundation-funded project (Grant No. 2012M510113). The authors are also grateful for financial resources from the National Key Technology R&D Programs (Nos. 2011BAG07B01 and 2012BAK24B04) and the PCSIRT (Grant No. IRT1029). They also acknowledge the anonymous reviewers who played a significant role in shaping and improving the manuscript.
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Published In
Journal of Engineering Mechanics
Volume 140 • Issue 3 • March 2014
Pages: 542 - 551
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jul 3, 2012
Accepted: May 23, 2013
Published online: May 25, 2013
Published in print: Mar 1, 2014
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