Sustained oscillation of flexible cantilevers without vortex shedding

The present work investigates the fluid-structure interaction (FSI) of a flexible cylindrical cantilever beam at subcritical Reynolds numbers ($Re$). A fully-coupled fluid-structure solver based on the three-dimensional (3D) incompressible Navier-Stokes equations and Euler-Bernoulli beam theory is employed to numerically examine the coupled dynamics of the beam. We assess the extent to which such a flexible cylindrical beam could sustain oscillations in this $Re$ regime when it is either exposed to a steady upstream wake (i.e., tandem cylinder configuration) or subjected to an externally applied base excitation. Our results indicate that within a particular range of reduced velocity parameter ($U^*$), the beam experiences sustained oscillations in both scenarios, leading to periodic vortex shedding downstream. The mechanism governing the sustained oscillations is characterized as synchronization, during which the frequency of the cross-flow fluid loading matches the beam's first-mode natural frequency. When the beam is subjected to base excitation, the critical Reynolds number for vortex shedding ($Re_{c}$) is found to reduce to $Re_{c}\approx5$. Above this threshold, vortex shedding is found to occur by stimulating the pair of counter-rotating vortices in the near-wake region. For the tandem cylinder configuration, the beam is shown to exhibit figure-eight-shaped tip motion trajectories during its oscillatory response. However, various patterns of tip motion trajectories, including figure-eight, and chaotic-type responses, are observed when the beam is under external base excitation. The findings of this work aim to generalize our understanding of sustained oscillation in flexible cylindrical cantilevers and have relevance to the development of bio-inspired cantilever flow sensors

A Finite Element-Inspired Hypergraph Neural Network: Application to Fluid Dynamics Simulations

An emerging trend in deep learning research focuses on the applications of graph neural networks (GNNs) for mesh-based continuum mechanics simulations. Most of these learning frameworks operate on graphs wherein each edge connects two nodes. Inspired by the data connectivity in the finite element method, we present a method to construct a hypergraph by connecting the nodes by elements rather than edges. A hypergraph message-passing network is defined on such a node-element hypergraph that mimics the calculation process of local stiffness matrices. We term this method a finite element-inspired hypergraph neural network, in short FEIH($\phi$)-GNN. We further equip the proposed network with rotation equivariance, and explore its capability for modeling unsteady fluid flow systems. The effectiveness of the network is demonstrated on two common benchmark problems, namely the fluid flow around a circular cylinder and airfoil configurations. Stabilized and accurate temporal roll-out predictions can be obtained using the $\phi$-GNN framework within the interpolation Reynolds number range. The network is also able to extrapolate moderately towards higher Reynolds number domain out of the training range

Self-sustained oscillations in whiskers without vortex shedding

Sensing the flow of water or air disturbance is critical for the survival of many animals: flow information helps them localize food, mates, and prey and to escape predators. Across species, many flow sensors take the form of long, flexible cantilevers. These cantilevers are known to exhibit sustained oscillations when interacting with fluid flow. In the presence of vortex shedding, the oscillations occur through mechanisms such as wake- or vortex-induced vibrations. There is, however, no clear explanation for the mechanisms governing the sustained oscillation of flexible cantilevers without vortex shedding. In recent work, we showed that a flexible cylindrical cantilever could experience sustained oscillations in its first natural vibration mode in water at Reynolds numbers below the critical Reynolds number of vortex shedding. The oscillations were shown to be driven by a frequency match (synchronization) between the flow frequency and the cantilever's first-mode natural frequency. Here, we use a body-fitted fluid-structure solver based on the Navier-Stokes and nonlinear structural equations to simulate the dynamics of a cantilevered whisker in the air at a subcritical value of Reynolds number. Results show that second-mode synchronization governs the whisker's sustained oscillation. Wavy patterns in the shear layer dominate the whisker's wake during the vibrations, indicating that parallel shear layers synchronize with the whisker's motion. As a result of this synchronization, oval-shaped motion trajectories, with matching streamwise and cross-flow vibration frequencies, are observed along the whisker. The outcomes of this study suggest possible directions for designing artificial bio-inspired flow sensors