Application of a parametric modal analysis approach to flexible-multibody systems

It is widely recognized that modal analysis is an effective tool for the study, modeling, design, control and understanding of mechanical systems. However, its applicability is limited to linear or linearized systems. The validity of linearized models is bounded in an infinitesimal neighborhood of the linearization point (operating point). A series of modal analysis is therefore required to calculate the system modal properties if the operating point varies, as in the case of multibody systems, which typically show gross motion. In order to reduce the computational effort required to solve a series of modal analysis, the parametric modal analysis method recently proposed by Wittmuess et al. (2016) has been applied to derive an analytical polynomial expression for the eigenpairs of a flexible multibody system in generalized coordinates. A numerical validation of a planar flexible manipulator is presented. It shows that the method allows for correctly approximating the modal content over a wide range of the generalized coordinates of the system while drastically reducing the computational effort.