Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation

Erbas, Baris; Kaplunov, Julius; Elishakoff, Isaac

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.

Citation

Erbas, B., Kaplunov, J., & Elishakoff, I. (2022). Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation. Mathematics and Mechanics of Solids, 27(9), 1638-1648. https://doi.org/10.1177/10812865211023885

• Journal Article Type: Article
• Acceptance Date: Jun 15, 2021
• Online Publication Date: Jun 15, 2021
• Publication Date: 2022-09
• Deposit Date: Jun 5, 2023
• Journal: MATHEMATICS AND MECHANICS OF SOLIDS
• Print ISSN: 1081-2865
• Publisher: SAGE Publications
• Peer Reviewed: Peer Reviewed
• Volume: 27
• Issue: 9
• Article Number: ARTN 10812865211023885
• Pages: 1638-1648
• DOI: https://doi.org/10.1177/10812865211023885