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In this work, we present a comprehensive experimental study on the problem of harmonic oscillations of rigid plates with H-shaped cross sections submerged in a quiescent, Newtonian, incompressible, viscous fluid environment. Motivated by recent results on the minimization of hydrodynamic damping for transversely oscillating flat plates, we conduct a detailed qualitative and quantitative experimental investigation of the flow physics created by the presence of the flanges, that is, the vertical segments in the plate cross section. Specifically, the main goal is to elucidate the effect of flange size on various aspects of fluid–structure interaction, by primarily investigating the dynamics of vortex shedding and convection. We perform particle image velocimetry experiments over a broad range of oscillation amplitudes, frequencies, and flange size-to-width ratios by leveraging the identification of pathlines, vortex shedding and dynamics, distinctive hydrodynamic regimes, and steady streaming. The fundamental contributions of this work include novel hydrodynamic regime phase diagrams demonstrating the effect of flange ratio on regime transitions, and in the investigation of their relation to qualitatively distinct patterns of vortex–vortex and vortex–structure interactions. Finally, we discuss steady streaming, identifying primary, and secondary structures as a function of the governing parameters. 

Abstract Numerous nanometrology techniques concerned with probing a wide range of frequency-dependent properties would benefit from a cantilevered sensor with tunable natural frequencies. In this work, we propose a method to arbitrarily tune the stiffness and natural frequencies of a microplate sensor for atomic force microscope applications, thereby allowing resonance amplification at a broad range of frequencies. This method is predicated on the principle of curvature-based stiffening. A macroscale experiment is conducted to verify the feasibility of the method. Next, a microscale finite element analysis is conducted on a proof-of-concept device. We show that both the stiffness and various natural frequencies of the device can be controlled through applied transverse curvature. Dynamic phenomena encountered in the method, such as eigenvalue curve veering, are discussed and methods are presented to accommodate these phenomena. We believe that this study will facilitate the development of future curvature-based microscale sensors for atomic force microscopy applications. 

In this study, we propose a novel plate-like sensor which utilizes curvature-based stiffening effects for enhanced nanometrology. In the proposed concept, the stiffness and natural frequencies of the sensor can be arbitrarily adjusted by applying a transverse curvature via piezoelectric actuators, thereby enabling resonance amplification over a broad range of frequencies. The concept is validated using a macroscale experiment. Then, a microscale finite element analysis is used to study the effect of applied curvature on the microplate static stiffness and natural frequencies. We show that imposed transverse curvature is an effective way to tune the in-situ static stiffness and natural frequencies of the plate sensor system. These findings will form the basis of future curvature-based stiffening microscale studies for novel scenarios in atomic force microscopy.