Equations for Nonlinear Analysis of 3D Motions of Beams

[+] Author and Article Information
M. R. M. Crespo da Silva

Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, New York 12180-3590

Appl. Mech. Rev 44(11S), S51-S59 (Nov 01, 1991) doi:10.1115/1.3121373 History: Online April 30, 2009


The formulation of a set of mathematically consistent differential equations for analyzing nonlinear flexural–flexural–torsional–extensional motions of an Euler–Bernoulli beam is presented. The beam may be mounted on a rotating or on a non–rotating base. A brief discussion on an Euler-like form of the equations is also presented. When the equations are expanded about their equilibrium solution to a desired order in an artificial “bookkeeping parameter” ε, the resulting equations are well suited for a perturbation analysis of the motion. Such analysis discloses a number of important nonlinear phenomena exhibited by the system. Order ε3 equations expanded about the zero equilibrium are also developed here.

Copyright © 1991 by American Society of Mechanical Engineers
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