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TECHNICAL PAPERS

The Role of Lagrangian Strain in the Dynamic Response of a Flexible Connecting Rod

[+] Author and Article Information
Jen-San Chen, Kwin-Lin Chen

Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617

J. Mech. Des 123(4), 542-548 (May 01, 1999) (7 pages) doi:10.1115/1.1415738 History: Received May 01, 1999
Copyright © 2001 by ASME
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References

Midha,  A., Erdman,  A. G., and Frohrib,  D. A., 1978, “Finite Element Approach to Mathematical Modeling of High Speed Elastic Linkages,” Mech. Mach. Theory, 13, pp. 603–618.
Shabana, A. A., 1989, Dynamics of Multibody Systems, John Wiley and Sons, New York.
Nagarajan,  S., and Turcic,  D. A., 1990, “General Methods of Determining Stability and Critical Speeds for Elastic Mechanism Systems,” Mech. Mach. Theory, 25, No. 2, pp. 209–223.
Neubauer,  A. H., Cohen,  R., and Hall,  A. S., 1966, “An Analytical Study of the Dynamics of an Elastic Linkage,” ASME J. Eng. Ind., 88, pp. 311–317.
Badlani,  M., and Midha,  A., 1982, “Member Initial Curvature Effects on the Elastic Slider-Crank Mechanism Response,” ASME J. Mech. Des., 104, pp. 159–167.
Badlani,  M., and Midha,  A., 1983, “Effect of Internal Material Damping on the Dynamics of a Slider-Crank Mechanism,” ASME J. Mech., Transm., Autom. Des., 105, pp. 452–459.
Badlani,  M., and Kleninhenz,  W., 1979, “Dynamic Stability of Elastic Mechanism,” ASME J. Mech. Des., 101, pp. 149–153.
Tadjbakhsh,  I. G., 1982, “Stability of Motion of Elastic Planar Linkages With Application to Slider Crank Mechanism,” ASME J. Mech. Des., 104, pp. 698–703.
Tadjbakhsh,  I. G., and Younis,  C. J., 1986, “Dynamic Stability of the Flexible Connecting Rod of a Slider Crank Mechanism,” ASME J. Mech., Transm., Autom. Des., 108, pp. 487–496.
Zhu,  Z. G., and Chen,  Y., 1983, “The Stability of the Motion of a Connecting Rod,” ASME J. Mech., Transm., Autom. Des., 105, pp. 637–640.
Viscomi,  B. V., and Ayre,  R. S., 1971, “Nonlinear Dynamic Response of Elastic Slider-Crank Mechanism,” ASME J. Eng. Ind., 93, pp. 251–262.
Hsieh,  S. R., and Shaw,  S. W., 1994, “The Dynamic Stability and Nonlinear Resonance of a Flexible Connecting Rod: Single Mode Model,” J. Sound Vib., 170, pp. 25–49.
Jasinski,  P. W., Lee,  H. C., and Sandor,  G. N., 1970, “Stability and Steady-State Vibrations in a High Speed Slider-Crank Mechanism,” ASME J. Appl. Mech., 37, pp. 1069–1076.
Jasinski,  P. W., Lee,  H. C., and Sandor,  G. N., 1971, “Vibrations of Elastic Connecting Rod of a High Speed Slider-Crank Mechanism,” ASME J. Eng. Ind., 93, pp. 636–644.
Chu,  S. C., and Pan,  K. C., 1975, “Dynamic Response of a High Speed Slider-Crank Mechanism With an Elastic Connecting Rod,” ASME J. Eng. Ind., 97, pp. 542–550.
Fung,  R.-F., and Chen,  H.-H., 1997, “Steady-State Response of the Flexible Connecting Rod of a Slider-Crank Mechanism With Time-Dependent Boundary Condition,” J. Sound Vib., 199, pp. 237–251.
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Figures

Grahic Jump Location
Schematic diagram of a slider and crank mechanism
Grahic Jump Location
Response g of the connecting rod at Ω=0.1. (1) Lagrangian strain formulation. (2) Solution predicted by Eq. (31).
Grahic Jump Location
Response f of the connecting rod at Ω=0.1
Grahic Jump Location
Envelope of response f of the connecting rod at Ω=0.1. (1) Lagrangian strain formulation. (2) Linear strain formulation. (3) Solution predicted by Eq. (30).
Grahic Jump Location
Response g of the connecting rod at Ω=0.8. (1) Lagrangian strain formulation. (2) Linear strain formulation. (3) Axial load by integrating axial equilibrium equation. (4) Time-dependent-only axial load formulation. (5) Response predicted by Eq. (42).
Grahic Jump Location
Response f of the connecting rod at Ω=0.8. (1) Lagrangian strain formulation. (2) Linear strain formulation.
Grahic Jump Location
Comparison of one-mode and two-mode approximations at Ω=0.8. (1) g from one-mode approximation. (2) g1 and (3) g2 from two-mode approximation.

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