The dynamic response of a BimorphR cantilever (10 mm × 1 mm × 0.5 mm) is investigated experimentally in air and in Fluorinet™ (3M™) liquids with varying viscosity but nearly the same density. The gap height d between the cantilever and a solid surface is varied from millimeter to micrometer range and the response of the cantilever is interpreted in terms of added mass ma and viscous damping coefficient cv. Key dimensionless parameters based on the Navier-Stokes (N-S) equations include the kinetic Reynolds number Rk = ωb2/4η (ω is the circular frequency and η the kinematic viscosity) and the dimensionless gap height d/b, where b is the cantilever width. The added mass increases (and resonance frequency decreases) with increasing fluid density and decreasing d/b, where the dimensionless gap height d/b has a stronger effect. The added mass coefficient is independent of Rk for Rk > 270 and d/b > 0.01. The N-S equations can be linearized when d/b > 0.1. In liquids, the viscous damping coefficient increases (and the Q-factor decreases) with increasing dynamic viscosity (decreasing Rk) and decreasing d/b. In general, the viscous terms in the N-S equations affect the viscous damping coefficient at all gaps. The implications of the results on sensor design are briefly discussed.
Bibliographical noteFunding Information:
The authors gratefully acknowledge support from the National Science Foundation (NSF/DMII-9978744).
- Cantilever beam
- Fluid-structure interaction
- Resonance frequency
- Viscous damping
- Wall effects