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Research Papers

Equations of Motion for an Inextensible Beam Undergoing Large Deflections

[+] Author and Article Information
Earl Dowell

Professor
Department of Mechanical Engineering and
Materials Science,
Duke University,
Durham, NC 27708
e-mail: earl.dowell@duke.edu

Kevin McHugh

Department of Mechanical Engineering and
Materials Science,
Duke University,
Durham, NC 27708
e-mail: kevin.mchugh@duke.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 14, 2016; final manuscript received February 15, 2016; published online March 10, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(5), 051007 (Mar 10, 2016) (7 pages) Paper No: JAM-16-1024; doi: 10.1115/1.4032795 History: Received January 14, 2016; Revised February 15, 2016

The Euler–Lagrange equations and the associated boundary conditions have been derived for an inextensible beam undergoing large deflections. The inextensibility constraint between axial and transverse deflection is considered via two alternative approaches based upon Hamilton's principle, which have been proved to yield equivalent results. In one approach, the constraint has been appended to the system Lagrangian via a Lagrange multiplier, while in the other approach the axial deflection has been expressed in terms of the transverse deflection, and the equation of motion for the transverse deflection has been determined directly. Boundary conditions for a cantilevered beam and a free–free beam have been considered and allow for explicit results for each system's equations of motion. Finally, the Lagrange multiplier approach has been extended to equations of motion of cantilevered and free–free plates.

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Grahic Jump Location
Fig. 1

(a) Cantilevered and (b) free–free beam configuration sketches to illustrate the evaluated system

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