Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation
College
Engineering and Computer Science
Department
Ocean and Mechanical Engineering
Document Type
Article
Publication/Event/Conference Title
Mathematics and Mechanics of Solids
Publication Status
Version of Record
Abstract
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.
First Page
1638
Last Page
1648
DOI
10.1177/10812865211023885
Publication Date
9-1-2022
Recommended Citation
Erbaş, Barış; Kaplunov, Julius; and Elishakoff, Isaac, "Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation" (2022). Faculty Scholarship. 195.
https://digitalcommons.fau.edu/faculty_papers/195