Bridging the Gap Between Nonlinear Normal Modes and Modal Derivatives

Nonlinear Normal Modes (NNMs) have a clear conceptual relation to the classical linear normal modes (LNMs), yet they offer a solid theoretical framework for interpreting a wide class of non-linear dynamical phenomena with no linear counterpart. The main difficulty associated with NNMs is that their calculation for large-scale models is expensive, particularly for distributed nonlinearities. Repeated direct time integrations need to be carried out together with extensive sensitivity analysis to reproduce the frequency-energy dependence of the modes of interest. In the present paper, NNMs are computed from a reduced model obtained using a quadratic transformation comprising LNMs and Modal Derivatives (MDs). Previous studies have shown that MDs can capture the essential dynamics of geometrically nonlinear structures and can greatly reduce the computational cost of time integration. A direct comparison with the NNMs computed from another standard reduction technique highlights the capability of the proposed reduction method to capture the essential nonlinear phenomena. The methodology is demonstrated using simple examples with 2 and 4 degrees of freedom.BeIPD-COFUND outgoing fellowship: Managing bifurcations of nonlinear mechanical systems using experimental continuation technique

Experimental modal analysis of nonlinear structures using broadband data

The objective of the present paper is to develop a rigorous identification methodology of nonlinear normal modes (NNMs) of engineering structures. This is achieved by processing experimental measurements collected under broadband forcing. The use of such a type of forcing signal allows to excite multiple NNMs simultaneously and, in turn, to save testing time. A two-step methodology integrating nonlinear system identification and numerical continuation of periodic solutions is proposed for the extraction of the individual NNMs from broadband input and output data. It is demonstrated using a numerical cantilever beam possessing a cubic nonlinearity at its free end. The proposed methodology can be viewed as a nonlinear generalization of the phase separation techniques routinely utilized for experimental modal analysis of linear structures. The paper ends with a comparison between this new nonlinear phase separation technique and a previously-developed nonlinear phase resonance method

Assessing the shear viscous behavior of continuous carbon fiber reinforced PEKK composites with squeeze flow measurements

Out-of-autoclave processes of carbon fiber thermoplastic composites are gaining interest as they can drastically reduce the economic cost. To optimize consolidation, the flow behavior of these highly filled composites has to be characterized. Here, we propose to measure viscosity of carbon fiber/polyetherketoneketone through squeeze flow experiments in a rheometer. A modified Stefan's law assuming a power law fluid behavior with full anisotropy is developed for square and circular geometries to model the data. Values of the power law parameters K and n are obtained, on the order of 15,000 Pa.sn and 0.02 at 1 bar. Though as expected independent of the samples' geometry and tapes' stacking, K and n depend on the applied pressure and plate size. This is due to localized shear which results in a shear-banding-like phenomenon. Finally, squeeze flow is compared to dynamic measurements and invalidate the Cox-Merz rule for such materials

Control of Metabolism and Growth Through Insulin-Like Peptides in Drosophila

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