Abstract :
Nonlinearities in the differential equations of motion of dynamical systems can play,
under certain conditions, such a dominant role that the motion described by linearized differential
equations bears no resemblance to the actual motion exhibited by the systems. For a structure,
nonlinearities are due to material behavior and to deformation. The latter are called "geometric
nonlinearities" and, even for linear (i.e., Hookean) materials and small deformations, their effect
can be dramatic. To investigate the nonlinear behavior of a dynamical system by making use of
analytical techniques, one must start the analysis by formulating a set of mathematically consistent
differential equations of motion for the system. Furthermore, the equations must be cast in a form
that makes them amenable to the application of known analytical methods, such as perturbation
techniques, to investigate the motion. The work presented in this paper addresses the formulation
of such equations for a class of multi-beam structures. Each beam in the structure may have arbitrary
cross section variation along its span, but behaves as inextensional. The structure may have any
number of beams and supports, and may carry any number of lumped masses along its span.
(~.;~ 1998 Published by Elsevier Science Ltd. All rights reserved
