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We propose a new theory for fluid–structure interactions of cantilever microbeams undergoing small amplitude vibrations in viscous fluids. The method is based on the concept of nonlocal modal hydrodynamic functions that accurately capture three-dimensional (3D) fluid loading on the structure. For short beams for which 3D effects become prominent, existing local theories based on two-dimensional (2D) fluid approximations are inadequate to predict the dynamic response. We discuss and compare model predictions in terms of frequency response functions, modal shapes, quality factors, and added mass ratios with the predictions of the local theory, and we validate our new model with experimental results.
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Theory of nonlocal modal hydrodynamic functions for beam and plate vibrations in viscous fluids
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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- Award ID(s):
- 1847513
- PAR ID:
- 10518137
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Journal of Fluids and Structures
- Volume:
- 126
- Issue:
- C
- ISSN:
- 0889-9746
- Page Range / eLocation ID:
- 104089
- 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/10.1016/j.jfluidstructs.2024.104089
