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Published October 14, 2016 | Published
Journal Article Open

Resonant frequencies of cantilevered sheets under various clamping configurations immersed in fluid

Abstract

Immersion of an elastic cantilevered sheet in a fluid can strongly affect its dynamic response. While significant effort has been expended in studying slender cantilevered sheets, the behavior of wide sheets has received far less attention. Here we study the clamping configuration's effect on the vibrational dynamics of wide cantilever sheets of macroscopic size, which naturally generate inviscid flows. Three practically relevant clamping configurations are investigated: clamping into (i) a thin and rigid horizontal plate, (ii) a rigid vertical wall, and (iii) a rigid line. These are found to produce different resonant frequencies, as expected from the nonlocal flows generated by these cantilevers. The resulting formulas are joined to an existing expression for slender cantilevers, leading to a universal formula valid for all aspect ratios (cantilever length/width) and mode numbers; accuracy is verified using finite element analysis. This study is expected to be of practical value in a host of engineering applications, such as those that utilize fluid-structure interactions for energy harvesting and aerodynamic design.

Copyright and License

© 2016 Author(s). Published by AIP Publishing.

Additional Information

The authors gratefully acknowledge the support of the Australian Research Council Grants Scheme. 

See supplementary material for numerical results for horizontal plate and vertical wall clamps that are analogous to Figs. 5 and 6, and the effect of finite thickness.

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Additional details

Created:
October 11, 2023
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October 11, 2023