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In this paper, we introduce a new nonlocal modal hydrodynamic theory for fluid–structure interactions (FSI) of light, flexible cantilever beams and plates undergoing small amplitude vibrations in Newtonian, incompressible, viscous, heavy fluids otherwise at rest. For low aspect ratio flexible structures and high mode numbers, three dimensional (3D) and nonlocal fluid effects become prominent drivers of the coupled dynamics, to the point that existing local hydrodynamic theories based on two dimensional (2D) fluid approximations become inadequate to predict the system response. On the other hand, our approach is based on a rigorous, yet efficient, 3D treatment of the hydrodynamic loading on cantilevered thin structures. The off-line solution of the FSI problem results in the so-called nonlocal modal hydrodynamic function matrix, that is, the representation of the nonlocal hydrodynamic load operator on a basis formed by the structural modes. Our theory then integrates the nonlocal hydrodynamics within a fully coupled structural modal model in the frequency domain. We compare and discuss our theory predictions in terms of frequency response functions, mode shapes, hydrodynamic loads, quality factors, added mass ratios with the predictions of the classical local approaches, for different actuation scenarios, identifying the limitations of the hypotheses underlying existing treatments. Importantly, we also validate our new model with experiments conducted on flexible square plates. While computationally efficient, our fully coupled theory is exact up to numerical truncation and can bridge knowledge gaps in the design and analysis of FSI systems based on low aspect ratio flexible beams and plates.
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Quantum hydrodynamic approximations to the finite temperature trapped Bose gases
For the quantum kinetic system modelling the Bose-Einstein Condensate that accounts for interactions between condensate and excited atoms, we use the Chapman-Enskog expansion to derive its hydrodynamic approximations, include both Euler and Navier-Stokes approximations. The hydrodynamic approximations describe not only the macroscopic behavior of the BEC but also its coupling with the non-condensates, which agrees with the Landau two-fluid theory.
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- Award ID(s):
- 1854453
- PAR ID:
- 10087167
- Date Published:
- Journal Name:
- Physica. D, Nonlinear phenomena
- Volume:
- 380–381
- Issue:
- 1
- ISSN:
- 0167-2789
- Page Range / eLocation ID:
- 45-57
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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