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A novel penalty-based reduced order modelling method for dynamic analysis of joint structures. (English) Zbl 1428.93031

Fehr, Jörg (ed.) et al., IUTAM symposium on model order reduction of coupled systems. MORCOS 2018. Proceedings of the IUTAM symposium, Stuttgart, Germany, May 22–25, 2018. Cham: Springer. IUTAM Bookser. 36, 165-176 (2020).
Summary: This work proposes a new reduced order modelling method to improve the computational efficiency for the dynamic simulation of a jointed structures with localized contact friction nonlinearities. We reformulate the traditional equation of motion for a joint structure by linearising the nonlinear system on the contact interface and augmenting the linearised system by introducing an internal nonlinear penalty variable. The internal variable is used to compensate the possible nonlinear effects from the contact interface. Three types of reduced basis are selected for the Galerkin projection, namely, the vibration modes (VMs) of the linearised system, static modes (SMs) and also the trial vector derivatives (TVDs) vectors. Using these reduced basis, it would allow the size of the internal variable to change correspondingly with the number of active nonlinear DOFs. The size of the new reduced order model therefore can be automatically updated depending on the contact condition during the simulations. This would reduce significantly the model size when most of the contact nodes are in a stuck condition, which is actually often the case when a jointed structure vibrates. A case study using a 2D joint beam model is carried out to demonstrate the concept of the proposed method. The initial results from this case study is then compared to the state of the art reduced order modeling.
For the entire collection see [Zbl 1425.93009].

MSC:

93B11 System structure simplification
93B18 Linearizations
93C10 Nonlinear systems in control theory
93-08 Computational methods for problems pertaining to systems and control theory
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