Modeling of three-dimensional beam nonlinear vibrations generalizing Hencky’s ideas

In this contribution, a novel nonlinear micropolar beam model suitable for metamaterials design in a dynamics framework is presented and discussed. The beam model is formulated following a completely discrete approach and it is fully defined by its Lagrangian, i.e., by the kinetic energy and by the potential of conservative forces. Differently from Hencky’s seminal work, which considers only flexibility to compute the buckling load for rectilinear and planar Euler–Bernoulli beams, the proposed model is fully three-dimensional and considers both the extensional and shear deformability contributions to the strain energy and translational and rotational kinetic energy terms. After having introduced the model formulation, some simulations obtained with a numerical integration scheme are presented to show the capabilities of the proposed beam model.

How intrusive are accelerometers for measuring nonlinear vibrations? A case study on a compressor blade subjected to vibro-impact dynamics

A characteristic feature of nonlinear vibrations is the energy transfer among different parts or modes of a mechanical system. Moreover, nonlinear vibrations are often non-periodic, even at steady state. To analyze these phenomena experimentally, the vibration response must be measured at multiple locations in a time-synchronous way. For this task, piezoelectric accelerometers are by far the most popular technology. While the effect of attached sensors on linear vibration properties is well-known (mass loading in particular), the purpose of the present work is to assess their intrusiveness on nonlinear vibrations. To this end, we consider a compressor blade that undergoes impacts near the tip for sufficiently large vibrations. We consider two configurations, one in which five triaxial piezoelectric accelerometers are glued to the blade surface and one without sensors attached. In both configurations, the vibration response is measured using a multi-point laser Doppler vibrometer. In the linear case without impacts, the lowest-frequency bending mode merely sees the expected slight frequency shift due to mass loading. In the nonlinear vibro-impact case, unexpectedly, the near-resonant response to harmonic base excitation changes severely both quantitatively and qualitatively. In particular, pronounced strongly modulated responses and period doubling are observed only in the case without attached sensors. We conjecture that this is due to a considerable increase of damping, caused by the sensor cables, affecting mainly the higher-frequency modes.

Study on Dynamic Snap-Through and Nonlinear Vibrations of an Energy Harvester Based on an Asymmetric Bistable Composite Laminated Shell

Bistable energy harvesters have been extensively studied. However, theoretical research on the dynamics of bistable energy harvesters based on asymmetric bistable composite laminated plate and shell structures has not been conducted. In this paper, a theoretical model on the dynamics of an energy harvester based on an asymmetric bistable composite laminated shell is established. The dynamic snap-through, the nonlinear vibrations and the voltage output with two potential wells of the bistable energy harvester are studied. The influence of the amplitude and the frequency for the base excitation on the bistable energy harvester is studied. When the frequency for the base excitation with a suitable amplitude in the frequency sweeping is located in a specific range or the amplitude for the base excitation with a suitable frequency in the amplitude sweeping is located in a specific range, the large-amplitude dynamic snap-through, nonlinear vibrations and voltage output with two potential wells can be found to occur. The amplitude and the frequency for the base excitation interact on each other for the specific amplitude or frequency range which migrates due to the softening nonlinearity. The vibration in the process of the dynamic snap-through behaves as the chaotic vibration. The nonlinear vibrations of the bistable system behave as the periodic vibration, the quasi-periodic vibration and the chaotic vibration. This study provides a theoretical reference for the design of energy harvesters based on asymmetric bistable composite laminated plate and shell structures.