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This work investigates the steady-state nonlinear dynamics of a large-deformation flexible beam model under oscillatory flow. A flexible beam dynamics model combined with hydrodynamic loading is employed using large deformation beam theory. The equations of motion discretised using the high-order finite element method (FEM) are solved in the time domain using the efficient Galerkin averaging-incremental harmonic balance (EGA-IHB) method. The arc-length continuation method and Hsu’s method trace stable and unstable solutions. The numerical results are in accordance with the physical experimental results and reveal multiple resonance phenomena. Low-order resonances exhibit hardening due to geometric nonlinearity, while higher-order resonances transition from softening to hardening influenced by inertia and geometric nonlinearity. A strong coupling between tensile and bending deformation is observed. The axial deformation is dominated by inertia, while bending resonance is influenced by an interplay between inertia, structure stiffness, and fluid drag. Finally, the effects of two dimensionless parameters, Keulegan and Carpenter number (KC) and Cauchy number (Ca), on the response of the flexible beam are discussed.
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Universal features of the shape of elastic fibres in shear flow
We present a numerical study of the dynamics of an elastic fibre in a shear flow at low Reynolds number, and seek to understand several aspects of the fibre's motion using the equations for slender-body theory coupled to the elastica. The numerical simulations are performed in the bead-spring framework including hydrodynamic interactions in two theoretical schemes: the generalized Rotne–Prager–Yamakawa model and a multipole expansion corrected for lubrication forces. In general, the two schemes yield similar results, including for the dominant scaling features of the shape that we identify. In particular, we focus on the evolution of an initially straight fibre oriented in the flow direction and show that the time scales of fibre bending, curling and rotation, which depend on its length and stiffness, determine the overall motion and evolution of the shapes. We document several characteristic time scales and curvatures representative of the shape that vary as power laws of the bending stiffness and fibre length. The numerical results are further supported by an interpretation using an elastica model.
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- Award ID(s):
- 1661672
- PAR ID:
- 10225330
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 914
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2020.1048
