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TECHNICAL PAPERS

Free Vibration Analysis of Planar Flexible Mechanisms

[+] Author and Article Information
S. D. Yu

Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Ontario, Canada M5B 2K3

F. Xi

Department of Aerospace Engineering, Ryerson University, Toronto, Ontario, Canada M5B 2K3

J. Mech. Des 125(4), 764-772 (Jan 22, 2004) (9 pages) doi:10.1115/1.1626130 History: Received June 01, 2001; Revised March 01, 2003; Online January 22, 2004
Copyright © 2003 by ASME
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References

Erdman,  A. G., and Sandor,  G. N., 1972, “Kineto-Elastodynamics—A Review of the State of the Art and Trends,” Mech. Mach. Theory, 7, pp. 19–33.
Huston,  R. L., 1981, “Multi-Body Dynamics Including the Effects of Flexibility and Compliance,” Comput. Struct., 14(5–6), pp. 443–451.
Shabana,  A. A., 1997, “Flexible Multibody Dynamics: Review of Past and Recent Developments,” Multibody System Dynamics,1(2), pp. 189–222.
Song,  J. O., and Haug,  E. J., 1980, “Dynamic Analysis of Planar Flexible Mechanisms,” Computer Methods in Applied Mechanics and Engineering,24, pp. 359–381.
Sadler,  J. P., 1975, “On the Analytical Lumped-Mass Model of an Elastic Four-Bar Mechanism,” ASME J. Eng. Ind., 97(2), pp. 561–565.
Cardona,  A., and Geradin,  M., 1991, “Modelling of Superelements in Mechanism Analysis,” Int. J. Numer. Methods Eng., 32, pp. 1565–1593.
Badlani, M. L., and Midha, A., 1979, “A Hierarchy of Equations of Motion of Planar Mechanism With Elastic Link,” Proceedings of the 6th Applied Mechanisms Conference, Denver, Colorado, pp. XXII-1-4.
Blejwas, T. E., 1979, “The Simulation of Elastic Mechanisms Using Kinematic Constraints and Lagrange Multipliers,” Proceedings of the 6th Applied Mechanisms Conference, Denver, Colorado, pp. XLIV-1-3.
Meijaard,  J. P., 1991, “Direct Determination of Periodic Solutions of the Dynamical Equations of Flexible Mechanisms and Manipulators,” Int. J. Numer. Methods Eng., 32, pp. 1691–1710.
Chandrupatla, T. R., and Belegundu, A. D., 1997, Introduction to Finite Element Methods in Engineering, 2nd ed., Prentice Hall, Upper Saddle River, NJ, pp. 393–395.
Yu,  S. D., and Cleghorn,  W. L., 2002, “Dynamic Instability Analysis of High-Speed Flexible Four-Bar Mechanisms,” Mech. Mach. Theory, 37, pp. 1261–1285.
Walker, J. S., 1991, Fast Fourier Transforms, CRC Press, Boca Raton.
Erdman, E., and Sandor, G. N., 1997, Mechanisms Design Volume I, Prentice Hall.
Meirovitch, L., 1997, Principles and Techniques of Vibrations, Prentice Hall, Upper Saddle River, NJ.
Bathe, K. J., 1996, Finite Element Procedures, Prentice Hall, Upper Saddle River, NJ.
Lu, Y. F., 1996, Dynamics of Flexible Multibody Systems, Higher Education Press, Beijing, 1st ed., pp. 415–420 (in Chinese).
Yoo,  H. H., and Shih,  S. H., 1998, “Vibration Analysis of Rotating Cantilever Beams,” J. Sound Vib., 212(5), pp. 807–828.

Figures

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Rigid body configuration of a planar four-bar crank-rocker mechanism
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Deformed versus rigid body configurations
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Deformed link and body-fixed coordinates
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The 1st structural vibration mode shape of the first example mechanism at ϕ2=0° (a) ANSYS, (b) current paper
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The 2nd structural vibration mode shape of the first example mechanism at ϕ2=0° (a) ANSYS, (b) current paper
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The 3rd structural vibration mode shape of the first example mechanism at ϕ2=0° (a) ANSYS, (b) current paper
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Variation of the first three natural frequencies of the first example mechanism throughout a cycle
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Variation of most prominent lateral displacements in the first three modal vectors of the first example mechanism throughout a cycle
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Harmonic compositions of the most prominent displacement in the modal vector of the first example mechanism
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A rotating cantilever beam
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Natural frequencies of a rotating cantilever beam
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The 1st dynamic natural frequency of the third example mechanism for five different crank speeds throughout a cycle
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The 2nd dynamic natural frequency of the third example mechanism for five different crank speeds throughout a cycle
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The 3rd dynamic natural frequency of the third example mechanism for five different crank speeds throughout a cycle
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The 4th dynamic natural frequency of the third example mechanism for five different crank speeds throughout a cycle
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The 5th dynamic natural frequency of the third example mechanism for five different crank speeds throughout a cycle

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