Analytic methods for the modeling of flexible structures

Abstract

Standard approaches to the modeling of large flexible structures, such as the Finite Element Method, are essentially based on small-scale approximation: the structure is thought of as consisting of many pieces that are small enough to have their dynamics approximated by a low-order model. This modeling philosophy is suitable for complicated and inhomogeneous structures, but becomes awkward when one has to do with structures that are built up from highly flexible but homogeneous parts. In the latter case, it would be much more natural to use partial differential equations. In this paper, we discuss some possible analytic approaches to the modeling of flexible structures, with an emphasis on the computation of the natural frequencies.