## Abstract

The dynamic response of a Bimorph^{R} 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 m_{a} and viscous damping coefficient c_{v}. Key dimensionless parameters based on the Navier-Stokes (N-S) equations include the kinetic Reynolds number R_{k} = ωb^{2}/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 R_{k} for R_{k} > 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 R_{k}) 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.

Original language | English (US) |
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Pages (from-to) | 240-254 |

Number of pages | 15 |

Journal | Sensors and Actuators, A: Physical |

Volume | 102 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2003 |

### Bibliographical note

Funding Information:The authors gratefully acknowledge support from the National Science Foundation (NSF/DMII-9978744).

## Keywords

- Cantilever beam
- Fluid-structure interaction
- Resonance frequency
- Viscous damping
- Wall effects