On the Coupling of Reduced Order Modeling with Substructuring of Structural Systems with Component Nonlinearities

Abstract

The emergence of digital virtualization has brought Reduced Order Models (ROM) into the spotlight. A successful reduced order representation should allow for modeling of complex effects, such as nonlinearities, and ensure validity over a domain of inputs. Parametric Reduced Order Models (pROMs) for nonlinear systems attempt to accommodate both previous requirements (Benner et al., SIAM Rev 57(4), 1–14, 2015). Our work addresses a physics-based reduced representation of structural systems with localized nonlinear features. Via implementation of the approach described in Quinn (J Sound Vib 331(1), 81–93, 2012), we achieve a substructuring formulation similar to Component Mode Synthesis. However, instead of individual component modes, reduction modes of a global nature are obtained from the corresponding linear monolithic system. In turn, this technique allows for a divide and conquer strategy that naturally couples the response between linear and nonlinear subdomains. A pROM able to exploit this modular formulation is developed as a next step. The framework treats each component independently, and individual projection bases are assembled by applying a Proper Orthogonal Decomposition (POD) on snapshots of each subdomain’s response. Parametric dependencies on the boundary conditions and the structural and excitation traits are injected into the pROM utilizing clustering, following the methodology in Vlachas et al. (Vlachas, K., Tatsis, K., Agathos, K., Brink, A.R., Chatzi, E.: A local basis approximation approach for nonlinear parametric model order reduction. Journal of Sound and Vibration 502, 116055, 2021). To this end, a modified strategy is employed, relying on the Modal Assurance Criterion as a measure to indicate optimal training samples while defining regions with similar underlying dynamics on the domain of parametric inputs. A numerical case study of a 3D wind turbine tower featuring material nonlinearities exemplifies our approach. The derived pROM offers an accelerated approximation of the underlying high fidelity response and can be utilized for numerous tasks, including vibration control, residual life estimation, and condition assessment of hotspot locations.