Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation
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Ad Hoc
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A two-dimensional mixed problem for a thin elastic strip resting on a Winkler foundation is considered within the framework of plane stress setup. The relative stiffness of the foundation is supposed to be small to ensure low-frequency vibrations. Asymptotic analysis at a higher order results in a one-dimensional equation of bending motion refining numerous ad hoc developments starting from Timoshenko-type beam equations. Two-term expansions through the foundation stiffness are presented for phase and group velocities, as well as for the critical velocity of a moving load. In addition, the formula for the longitudinal displacements of the beam due to its transverse compression is derived.
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1996 ◽
Vol 24
(2)
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pp. 67-75
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Keyword(s):
1936 ◽
Vol 41
(3)
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pp. 287
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2005 ◽
Vol 49
(3)
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pp. 305-321
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Keyword(s):
2021 ◽
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