On the Nonlinear Modeling of the Dynamics of Beams and Multi-Beam Structures
by
M.R.M. Crespo da Silva
Dept. of Mechanical Engrg., Aero. Engrg., and Mechanics; Rensselaer Polytechnic Institute; Troy, N.Y. 12180-3590

A number of papers dealing with analytical investigations of nonlinear response of a single member structure such as a beam, a plate, or a shell, can now be found in the literature. For complex structures that are made of several interconnected members, such investigations have been confined to the use of numerical methods. This is due to the difficulty associated with developing nonlinear differential equation models to represent the system. In this paper, the development of an analytical model for a particular class of multi-beam structures is presented. First, a review of the development of a set of mathematically consistent nonlinear differential equations that govern the dynamics of a single beam is presented. This is followed by the generalization of the work to a class of multi-beam structures. The methodology combines the advantage of numerical methods, which are used for generating values for the coefficients of all the terms that explicitly appear in the differential equations, and of analytical methods, which are used for investigating the nonlinear motion. Analytical investigations provide significant insight into how and why the structure may behave in certain ways that cannot be predicted by linearization of the differential equations. Several specific examples are also presented.

Date received: January 14, 2000