Structure Dynamics

Research in structural dynamics are devoted to thin structures (beams, plates and shells) vibrating at large amplitudes (i.e. comparable to the thickness). These vibration amplitudes are often encountered in practical applications such as aeronautics (plane wings, helicopter blades) or civil engineering (suspended bridge cables). The geometric nonlinearity give rise to complex phenomena that have to be finely predicted  and controled via fully nonlinear analyses. The main research axis are twofolds:

- Analysis of nonlinear dynamics, with particular emphasis to the transition from periodic to chaotic vibratory motions. For large plates, the concept of wave turbulence is also addressed to describe the dynamics. Analytical and numerical models are developped for thin plates and shells, so as to determine the critical values for excitation of modal couplings, giving rise to energy transfer between modes and quasi-periodic responses.

- Development of reduced-order models by using Nonlinear Normal Modes (NNMs). The geometric nonlinearity give rise to nonlinear coupling terms so that relevant numerical truncation are difficult to obtain. We use NNMs as a basis for reducing the nonlinear dynamics. They are defined as invariant manifolds in phase space, hence continuing the linear modes, which makes them the best possible candidates for reduced basis containing the most important dynamical features.

Finally, nonlinear material laws are also studied in collaboration with the MS group, with a particular emphasis on shape-memory alloys.