On the modal analysis of nonlinear beam and shell structures with singular mass and stiffness matrices

A complex structural system can be described by a collection of individual rigid and/or flexible components in combination with a set of kinematic constraints. Moreover, their configuration can be described by redundant coordinates yielding to singular system matrices. Therefore, the calculation of frequencies and modes using a classical modal analysis is not longer applicable. In this work, we propose a variational-consistent framework, which is able to deal with structural systems with singular matrices and relies on a null-space projection. Finally, the effectivity of the proposed framework is tested succesfully by complex examples (single- and multibody systems) containing rigid bodies, geometrically exact beams and solid-degenerate shells.