An Efficient Coupled Modal Quasi-static Approach for Characterizing Non-linear Modal Properties of Prestressed Structures

Linear modal analysis is a powerful tool in studying linear dynamical systems with several Degrees-of-Freedom (DoFs). There has been an increasing interest in how this can be extended to large (in the sense of number of DoFs) non-linear dynamical systems. The current study proposes an extension to the stationarity of Rayleigh quotients, a classical technique for linear modal analysis, and demonstrates its applicability to conservative and non-conservative non-linear systems. Apart from offering a theoretical motivation of modal analysis in non-linear dynamics, the approach also circumvents several limitations in previous quasi-static non-linear modal analysis methods. The method is demonstrated on a simplified model of a bolted-joint which includes unilateral springs and elastic dry friction elements describing the non-linearities. The results are compared with the Extended Periodic Motion Concept (EPMC), a frequency domain approach based on periodic solutions.