Resonant Characteristics of Rectangular Microcantilevers Vibrating Torsionally in Viscous Liquid Media

Document Type

Conference Proceeding



Format of Original

6 p.

Publication Date



Institute of Electrical and Electronics Engineers (IEEE)

Source Publication

2012 IEEE International Frequency Control Symposium

Source ISSN


Original Item ID

doi: 10.1109/FCS.2012.6243700


The resonant characteristics of rectangular microcantilevers vibrating in the torsional mode in viscous liquid media are investigated. The hydrodynamic load (torque per unit length) on the vibrating beam due to the liquid was first determined using a finite element model. An analytical expression of the hydrodynamic function in terms of the Reynolds number and aspect ratio, h/b (with thickness, h, and width, b) was then obtained by fitting the numerical results. This allowed for the resonance frequency and quality factor to be investigated as functions of both beam geometry and medium properties. Moreover, the effects of the aspect ratio on the cross-section's torsional constant, K, which affects the microcantilever's torsional stiffness, and on its polar moment of inertia, Jp, which is associated with the beam's rotational inertia, are also considered when obtaining the resonance frequency and quality factor. Compared with microcantilevers under out-of-plane (transverse) flexural vibration, the results show that microcantilevers that vibrate in their 1st torsional or 1st in-plane (lateral) flexural resonant modes have higher resonance frequency and quality factor. The increase in resonance frequency and quality factor results in higher mass sensitivity and reduced frequency noise, respectively. The improvement in the sensitivity and quality factor are expected to yield much lower limits of detection in liquid-phase chemical sensing applications.


Published as part of the proceedings of the conference, 2012 IEEE International Frequency Control Symposium, 2012: 1-6. DOI.