Finite Dimension Models of Flexible Structures

The paper presents a novel method for deriving approximated finite dimensional models for infinite-dimensional transfer functions that describe the dynamic behavior of flexible structures. The exact transfer function from a point force excitation to a point displacement or velocity, which is derived directly from the wave equation contains delays, corresponding to the traveling waves. The standard and convenient form for analysis and control is a rational transfer function. To overcome this discrepancy, an approximate, rational, finite dimensional model is sought. One approach is spatial discretization where the most common way is the well-known finite element method (FEM). In this work we introduce an alternative method that starts from the exact model and uses Padé approximation for the delay terms. The Padé based approximation (PBA) method is conceptually and technically completely different than FEM. It is shown that it preserves fundamental properties of the exact model and yields better approximations of the time and frequency responses..