Abstract
The oscillation of a thin blade immersed in a viscous fluid has received considerable attention recently due to its importance in technological applications such as the atomic force microscope and microelectromechanical systems. In this article, we consider the general case of a flexible thin blade executing spatially varying small amplitude oscillations in a viscous fluid. Exact analytical solutions for the three-dimensional flow field and hydrodynamic load are derived for both normal and torsional oscillations of arbitrary wave number. This contrasts previous investigations that focus exclusively on the complementary rigid-blade problem, which is two-dimensional, and rely on computational techniques.
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