Authors: Adrien Martin ^1,2,3,4; Andrea Opreni ⁵; Alessandra Vizzaccaro ⁶; Marielle Debeurre ^7,8; Loic Salles ^9,10; Attilio Frangi ⁵; Olivier Thomas ^7,8; Cyril Touzé ^1,2,3,4

• 1 Institut des Sciences de la mécanique et Applications industrielles
• 2 École Nationale Supérieure de Techniques Avancées
• 3 Institut Polytechnique de Paris
• 4 Institut des Sciences de la Mécanique et Applications Industrielles [IMSIA]
• 5 Politecnico di Milano [Milan]
• 6 University of Bristol [Bristol]
• 7 Laboratoire d’Ingénierie des Systèmes Physiques et Numériques [HESAM]
• 8 HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université
• 9 Imperial College London
• 10 Université de Liège

The direct parametrisation method for invariant manifolds is a nonlinear reduction technique which derives nonlinear mappings and reduced-order dynamics that describe the evolution of dynamical systems along a low-dimensional invariant-based span of the phase space. It can be directly applied to finite element problems. When the development is performed using an arbitrary order asymptotic expansion, it provides an efficient reduced-order modeling strategy for geometrically nonlinear structures. It is here applied to the case of rotating structures featuring centrifugal effect. A rotating cantilever beam with large amplitude vibrations is first selected in order to highlight the main features of the method. Numerical results show that the method provides accurate reduced-order models (ROMs) for any rotation speed and vibration amplitude of interest with a single master mode, thus offering remarkable reduction in the computational burden. The hardening/softening transition of the fundamental flexural mode with increasing rotation speed is then investigated in detail and a ROM parametrised with respect to rotation speed and forcing frequencies is detailed. The method is then applied to a twisted plate model representative of a fan blade, showing how the technique can handle more complex structures. Hardening/softening transition is also investigated as well as interpolation of ROMs, highlighting the efficacy of the method.

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