Nonlinear dynamics of highly flexible slender beams : efficient numerical strategies in the frequency domain ; Vibrations non linéaires de structures élancées hautement flexibles : stratégies numériques efficaces dans le domaine fréquentiel

The study of highly flexible slender beam structures such as cables, wires, hoses, turbine, engine and rotor blades, ropes, flexible rulers and wings has been of great interest in recent years due to their widespread use in modern industry. These flexible structures are found extensively in automotive and aerospace manufacturing, public transportation, robotics, micro- and nano-electromechanical systems (MEMS/NEMS) and even bio-inspired and biomechanics. The unique geometry of these structures takes the form of a beam where one dimension, typically the length, is exceedingly large compared to the two others. This geometry leads to a very low bending stiffness while the axial stiffness remains relatively high, so that these so-called highly flexible beams are capable of reaching extreme amplitudes of displacement. At very large amplitudes, so-called geometrical nonlinearities tied to the rotations of the cross-sections of the beam enter into the equations of motion, nonlinearities that cannot be simplified with any accuracy at such large amplitudes. In such cases, the geometrically exact beam model is often used to model the mechanics of the structure since it exactly preserves the geometrical nonlinearities up to any amplitude of motion. In this work, we are interested in studying the periodic oscillations of these highly nonlinear systems at extreme amplitudes of vibration. To this end, a finite element discretization of the geometrically exact beam model is realized. The finite element model is solved entirely in the frequency domain to target periodic solutions with a strong focus on computational efficiency. The numerical strategy presented in this work is capable of modeling highly flexible beam structures both in 2D and in 3D. Also included in this work concludes is an experimental validation of the numerical strategy involving dedicated experiments in vibration control. ; L'étude des structures de poutres élancées hautement flexibles telles que les câbles, les fils, les tuyaux, les pales de turbine, de ...