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TECHNICAL BRIEFS

Mathematical Model for Large Deflection Dynamics of a Compliant Beam Device

[+] Author and Article Information
Michael J. Panza

Mechanical Engineering, Gannon University, Erie, PA 16541

J. Dyn. Sys., Meas., Control 123(2), 283-288 (Sep 29, 1999) (6 pages) doi:10.1115/1.1367266 History: Received September 29, 1999
Copyright © 2001 by ASME
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References

Ananthasuresh, G. K., and Kota, S., 1995, “Designing Compliant Mechanisms,” Mech. Eng. (Am. Soc. Mech. Eng.), Nov., pp. 93–96.
Bisshopp,  K. E., and Drucker,  D. c., 1945, “Large Deflection of Cantilever Beams,” Q. Appl. Math., 3, No. 3, pp. 272–275.
Shoup,  T. E., 1972, “On the Use of the Nodal Elastica for the Analysis of Flexible Link Devices,” ASME J. Eng. Ind, , Aug., pp. 871–875.
Howell,  L. L., and Midha,  A., 1995, “Parametric Deflection Approximations for End-Loaded Large-Deflection Beams in Compliant Mechanisms,” ASME J. Mech. Des., 117, pp. 156–165.
Howell,  L. L., Midha,  A., and Norton,  T. W., 1996, “Evaluation of Equivalent Spring Stiffness for Use in a Pseudo-Rigid-Body Model of Large-Deflection Compliant Mechanisms,” ASME J. Mech. Des., 118, pp. 126–131.
Jensen, B. D., Howell, L. L., Gunyan, D. B., and Salmon, L. G., 1997 “The Design and Analysis of Compliant MEMS Using the Pseudo-Rigid-Body Model,” Proceedings, Microelectromechanical Systems, ASME International Mechanical Engineering Congress and Exposition, Dallas, DSC-Vol. 62, pp. 119–126.
Lyon, S. M., Evans, M. S., Erickson, P. A., and Howell, L. L., 1997, “Dynamic Response of Compliant Mechanisms Using the Pseudo-Rigid-Body Model,” Proceedings, ASME Design Engineering Technical Conferences, Sacramento, Sept.
Saxena,  A., and Kramer,  S. N., 1998, “A simple and Accurate Method for Determining Large Deflections in Compliant Mechanisms Subjected to End forces and Moments,” ASME J. Mech. Des., 120, pp. 392–400.
Crespo da Silva,  M. R. M., and Glynn,  C. C., 1978, “Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams, I. Equations of Motion, and II. Forced Motion,” Journal of Structural Mechanics, 6, No. 4, pp. 437–461.
Nayfeh,  A. H., Chin,  C., and Nayfeh,  S. A., 1995, “Nonlinear Normal Modes of a Cantilever Beam,” ASME J. Vibr. Acoust., 117, pp. 477–481.
Atanackovic,  T. M., and Cveticanin,  L. J., 1996, “Dynamics of Plane Motion of an Elastic Rod,” ASME J. Appl. Mech., 63, pp. 392–398.
Moon, F. C., 1987, Chaotic Vibrations, An Introduction for Applied Scientists and Engineers, Wiley, NY, pp. 96–97.
Popov, E. P., Mechanics of Materials, Prentice-Hall, New Jersey, 1976, p. 359.
Panza,  M. J., and Mayne,  R. W., 1996, “Hydraulic Actuator Tuning in the Control of A Rotating Beam Mechanism,” ASME J. Dyn. Syst., Meas., Control, 118, pp. 449–456.

Figures

Grahic Jump Location
Effect of dissipative terms on dynamic deflection
Grahic Jump Location
Dynamic deflection of system
Grahic Jump Location
Static deflection of beam
Grahic Jump Location
Free body diagram of tip mass

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