Nonlocal Theory for Submerged Cantilever Beams Undergoing Torsional Vibrations

Abstract

Abstract 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.