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

被引：14

作者：

Erbas, Baris ^{[1
]}

Kaplunov, Julius ^{[2
,3
]}

Elishakoff, Isaac ^{[4
]}

机构：

[1] Eskisehir Tech Univ, Dept Math, Yunus Emre Campus, TR-26470 Eskisehir, Turkey

[2] Keele Univ, Sch Comp & Math, Keele, Staffs, England

[3] Russian Acad Sci, Inst Problems Mech Engn, St Petersburg 196140, Russia

[4] Florida Atlantic Univ, Dept Ocean & Mech Engn, Boca Raton, FL 33431 USA

来源：

MATHEMATICS AND MECHANICS OF SOLIDS | 2022年 / 27卷 / 09期

基金：

俄罗斯科学基金会;

关键词：

Timoshenko beam; Winkler foundation; asymptotic; moving load; higher order; PLATE-BENDING EQUATION; TIMOSHENKO BEAM;

D O I：

10.1177/10812865211023885

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

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.

引用

页码：1638 / 1648

页数：11

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