MIXED LAGRANGIAN FORMULATION FOR MODELLING THE NON-SMOOTH BEHAVIOR OF CLUTCHING INERTER - Zhang,Y; Lavan,O; Málaga-Chuquitaype,C (2024)
Clutched inerter dampers (CID), represent a novel improvement on inerter dampers (ID) that has shown great potential for suppressing structural vibrations under severe ground-motions. However, the inherent nonlinearity and discontinuity of the clutching phenomena in CIDs can create significant difficulties for their accurate numerical modelling. In general, conventional existing methods either oversimplify the physics involved in dynamic contact or are inherently unstable, requiring excessive computing power. The Mixed Lagrangian Formulation (MLF), developed over the years, has shown to be a powerful tool for simulating non-smooth dynamics. In this context, this paper presents an alternative way of modelling structures equipped with CIDs. A proposed clutching inerter element, consisting of an inerter and a plasticity element, is introduced into the MLF framework. Then, the proposed formulation is validated through a simple numerical example, from which the results are compared to those from existing models used for clutching inerter. Finally, the advantages of MLF model and some implications on the modelling of clutched inerters are discussed.