Research Papers: Fundamental Issues and Canonical Flows

Thrust Force Characterization of Oscillating Cantilevers Operating Near Resonance

[+] Author and Article Information
Andrew Eastman

Department of Mechanical Engineering
and Materials Science,
University of Pittsburgh,
206 Benedum Hall,
3700 O'Hara Street,
Pittsburgh, PA 15261

Mark L. Kimber

Department of Mechanical Engineering
and Materials Science,
University of Pittsburgh,
206 Benedum Hall,
3700 O'Hara Street,
Pittsburgh, PA 15261
e-mail: mlk53@pitt.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received July 26, 2013; final manuscript received February 3, 2014; published online May 6, 2014. Assoc. Editor: Prashanta Dutta.

J. Fluids Eng 136(7), 071206 (May 06, 2014) (7 pages) Paper No: FE-13-1453; doi: 10.1115/1.4026667 History: Received July 26, 2013; Revised February 03, 2014

Harmonic oscillations from cantileverlike structures have found use in applications ranging from thermal management to atomic force microscopy and propulsion, due to their simplicity in design and ease of implementation. In addition, making use of resonance conditions, a very energy efficient solution is achievable. This paper focuses on the application of providing thrust through cantilever oscillations at or near the first mode of resonance. This method of actuation provides a balance between full biomimicry and ease of fabrication. Previous studies have shown promise in predicting the propulsion performance based on the operating parameters, however, they have only considered a single cantilever geometry. Here, additional cantilever sizes and materials are included, yielding a much larger design space to characterize the thrust trends. The thrust data is experimentally captured and is assembled into two sets of predictive correlations. The first is based on Reynolds and Strouhal numbers, while the second only employs the Keulegan–Carpenter number. Both correlations are proven to predict the experimental data and can be shown to yield nearly identical proportional relationships after accounting for the cantilever frequency response. The findings presented in this research will aid in further understanding and assessing the capabilities of thrust generation for oscillating cantilevers, but also provides a foundation for other applications such as convection heat transfer and fluid transport.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Binnig, G., Quate, C. F., and Gerber, C., 1986, “Atomic Force Microscope,” Phys. Rev. Lett., 56(9), pp. 930–933. [CrossRef] [PubMed]
Sfakiotakis, M., Lane, D. M., and Davies, B. C., 1999, “Review of Fish Swimming Modes for Aquatic Locomotion,” J. Oceanic Eng., 24(2), pp. 237–252. [CrossRef]
Kosa, G., Shoham, M., and Zaaroor, M., 2007, “Propulsion Method for Swimming Microrobots,” IEEE Trans. Robotics, 23(1), pp. 137–150. [CrossRef]
Low, K. H., Yang, J., Pattathil, A. P., and Zhang, Y., 2006, “Initial Prototype Design and Investigation of an Undulating Body by SMA,” Proceedings of the IEEE International Conference on Automation Science and Engineering, Shanghai, (pp. 472–477). [CrossRef]
Chung, H. C., Kummari, K. L., Croucher, S. J., Lawson, N. J., Guo, S., and Huang, Z., 2008, “Coupled Piezoelectric Fans With Two Degree of Freedom Motion for the Application of Flapping Micro Aerial Vehicles,” Sens, Actuators, A, 147(2), pp. 607–612. [CrossRef]
Ming, A., Park, S., Nagata, Y., and Shimojo, M., 2009, “Development of Underwater Robots Using Piezoelectric Fiber Composite,” Proceedings of the 2009 IEEE International Conference on Robotics and Automation (ICRA), Kobe, Japan, pp. 3821–3826. [CrossRef]
Toda, M. and Osaka, S., 1979, “Vibrational Fan Using Piezoelectric Polymer PVF2,” Proceedings of the IEEE, 67(8), pp. 1171–1173. [CrossRef]
Yoo, J. H., Hong, J. I., and Cao, W., 2000, “Piezoelectric Ceramic Bimorph Coupled to Thin Metal Plate as Cooling Fan for Electronic Devices,” Sens. Actuators, A, 79(1), pp. 8–12. [CrossRef]
Acikalin, T., Wait, S. M., Garimella, S. V., and Raman, A., 2004, “Experimental Investigation of the Thermal Performance of Piezoelectric Fans,” Heat Transfer Eng., 25(1), pp. 4–14. [CrossRef]
Acikalin, T., Garimella, S. V., Raman, A., and Petroski, J., 2007, “Characterization and Optimization of the Thermal Performance of Miniature Piezoelectric Fans,” Int. J. Heat Fluid Flow, 28(4), pp. 806–820. [CrossRef]
Kimber, M. and Garimella, S. V., 2009, “Measurement and Prediction of the Cooling Characteristics of a Generalized Vibrating Piezoelectric Fan,” Int. J. Heat Mass Transfer, 52(19–20), pp. 4470–4478. [CrossRef]
Eastman, A., Kiefer, J., and Kimber, M., 2012, “Thrust Measurements and Flow Field Analysis of a Piezoelectrically Actuated Oscillating Cantilever,” Exp. Fluids, 53(5), pp. 1533–1543. [CrossRef]
Kim, Y. H., Wereley, S. T., and Chun, C. H., 2004, “Phase-Resolved Flow Field Produced by a Vibrating Cantilever Plate Between Two Endplates,” Phys. Fluids, 16(1), pp. 145–162. [CrossRef]
Keulegan, G. H. and Carpenter, L. H., 1958, “Forces of Cylinders and Plates in an Oscillating Fluid,” J. Res. Natl. Bur. Stand. (U.S.), 60(5), pp. 423–440. [CrossRef]
Jordan, T., Ounaies, Z., Tripp, J., and Tcheng, P., 1999, “Electrical Properties and Power Considerations of a Piezoelectric Actuator,” MRS Proc., 604(1), pp. 203–208. [CrossRef]
Eastman, A. and Kimber, M., 2014, “Flow Shaping and Thrust Enhancement of Sidewall Bounded Oscillating Cantilevers,” Int. J. Heat Fluid Flow (submitted).
Kimber, M. and Garimella, S. V., 2009, “Cooling Performance of Arrays of Vibrating Cantilevers,” ASME J. Heat Transfer, 131(11), p. 111401. [CrossRef]


Grahic Jump Location
Fig. 1

General illustration of a typical piezoelectric fan with important dimensions included

Grahic Jump Location
Fig. 2

Visual representation of the size and shape of all the fans used for thrust measurements

Grahic Jump Location
Fig. 3

Graphical representation of the orientation and position of the thrust measurement setup

Grahic Jump Location
Fig. 4

Comparison of the previously collected data from Ref. [12] and the new data

Grahic Jump Location
Fig. 5

Thrust data for each fan compared to their respective amplitude ranges

Grahic Jump Location
Fig. 6

The nondimensional thrust for each fan compared to their respective amplitude ranges

Grahic Jump Location
Fig. 7

The nondimensional thrust with the curve fit using ghe Reynolds and Strouhal numbers

Grahic Jump Location
Fig. 8

The nondimensional thrust with the curve fit using the Keulegan–Carpenter number only

Grahic Jump Location
Fig. 9

Nondimensional thrust as a function of the Keulegan–Carpenter number



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In