The hydrodynamic loading of elastic microcantilevers vibrating in viscous fluids is analyzed computationally using a three-dimensional, finite element fluid-structure interaction model. The quality factors and added mass coefficients of several modes are computed accurately from the transient oscillations of the microcantilever in the fluid. The effects of microcantilever geometry, operation in higher bending modes, and orientation and proximity to a surface are analyzed in detail. The results indicate that in an infinite medium, microcantilever damping arises from localized fluid shear near the edges of the microcantilever. Closer to the surface, however, the damping arises due to a combination of squeeze film effects and viscous shear near the edges. The dependence of these mechanisms on microcantilever geometry and orientation in the proximity of a surface are discussed. The results provide a comprehensive understanding of the hydrodynamic loading of microcantilevers in viscous fluids and are expected to be of immediate interest in atomic force microscopy and microcantilever biosensors.

A mathematical model is presented to predict the oscillating dynamics of atomic force microscope cantilevers with nanoscale tips tapping on elastic samples in liquid environments. Theoretical simulations and experiments performed in liquids using low stiffness probes on hard and soft samples reveal that, unlike in air, the second flexural mode of the probe is momentarily excited near times of tip-sample contact. The model also predicts closely the tip amplitude and phase of the tip at different set points.

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We analyze the hydrodynamic coupling between long, slender micromechanical beams ͑microbeams͒ deployed in an array and oscillating in a viscous, incompressible fluid. The unsteady Stokes equations are solved using a boundary integral technique in a two-dimensional plane containing the microbeam cross sections. The oscillations of nearest neighbor and the next neighbor microbeams couple hydrodynamically in unanticipated ways depending on the gap, frequency, and the relative phase and amplitude of their oscillation. A rational basis is provided for choosing the gap between neighboring microbeams in an array in order to either decouple their hydrodynamics or to couple them strongly. The results clearly suggest that the dynamics of microbeams in an array can be tuned in a cooperative manner so as to minimize or maximize the hydrodynamic resistance on individual microbeams.

Abstract-Piezoelectric fans are gaining in popularity as lowpower-consumption and low-noise devices for the removal of heat in confined spaces. The performance of piezoelectric fans has been studied by several authors, although primarily at the fundamental resonance mode. In this article the performance of piezoelectric fans operating at the higher resonance modes is studied in detail. Experiments are performed on a number of commercially available piezoelectric fans of varying length. Both finite element modeling and experimental impedance measurements are used to demonstrate that the electromechanical energy conversion (electromechanical coupling factors) in certain modes can be greater than in the first bending mode; however, losses in the piezoceramic are also shown to be higher at those modes. The overall power consumption of the fans is also found to increase with increasing mode number.Detailed flow visualizations are also performed to understand both the transient and steady-state fluid motion around these fans. The results indicate that certain advantages of piezoelectric fan operation at higher resonance modes are offset by increased power consumption and decreased fluid flow.