The ESR will investigate the nonlinear dynamics of slender beams in large rotation nonlinear dynamics. New modelling strategies will be based on the coupling of quaternions (for rotation parametrisation) / finite elements (for discretisation) / asymptotic numerical method (for continuation) and the harmonic balance method (to get periodic solutions). Then, reduced order modelling (nonlinear normal mode concept) will be used to reduce the dynamics and obtain accurate numerical solutions. Targeted industrial applications will be nonlinear vibration absorbers, for which the stiffness of the absorber will be realised by prestressed beams. The numerical part of the work will be implemented in an open source software package based on the MANLAB solver.
Firstly, original and efficient numerical strategies for the nonlinear dynamics of beams in the frequency domain will be available at the end of the ESR PhD. Secondly, the special concept of nonlinear modes will be applied for the first time to those problems and tested to reduce the dynamics and also give physical insights in the phenomena