Research Papers

Vibration Analysis of the Flexible Connecting Rod With the Breathing Crack in a Slider-Crank Mechanism

[+] Author and Article Information
Yan-Shin Shih

Department of Mechanical Engineering,
Chung Yuan Christian University,
Chung-Li 32023, Taiwan
e-mail: ysshih@cycu.edu.tw

Chen-Yuan Chung

Department of Mechanical and Aerospace
Case Western Reserve University,
Cleveland, OH 44106
e-mail: zhen-yuan@alu.cycu.edu.tw

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received November 4, 2012; final manuscript received March 12, 2013; published online June 19, 2013. Assoc. Editor: Corina Sandu.

J. Vib. Acoust 135(6), 061009 (Jun 19, 2013) (9 pages) Paper No: VIB-12-1306; doi: 10.1115/1.4024053 History: Received November 04, 2012; Revised March 12, 2013

This paper investigates the dynamic response of the cracked and flexible connecting rod in a slider-crank mechanism. Using Euler–Bernoulli beam theory to model the connecting rod without a crack, the governing equation and boundary conditions of the rod's transverse vibration are derived through Hamilton's principle. The moving boundary constraint of the joint between the connecting rod and the slider is considered. After transforming variables and applying the Galerkin method, the governing equation without a crack is reduced to a time-dependent differential equation. After this, the stiffness without a crack is replaced by the stiffness with a crack in the equation. Then, the Runge–Kutta numerical method is applied to solve the transient amplitude of the cracked connecting rod. In addition, the breathing crack model is applied to discuss the behavior of vibration. The influence of cracks with different crack depths on natural frequencies and amplitudes is also discussed. The results of the proposed method agree with the experimental and numerical results available in the literature.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Lowen, G. G., and Jandrasits, W. G., 1972, “Survey of Investigations Into the Dynamic Behavior of Mechanisms Containing Links With Distributed Mass and Elasticity,” Mech. Mach. Theory, 7(1), pp. 3–17. [CrossRef]
Erdman, A. G., Sandor, G. N., and Oakberg, R. G., 1972, “A General Method for Kineto-Elastodynamic Analysis and Synthesis of Mechanisms,” J. Eng. Ind., 94(4), pp. 1193–1205. [CrossRef]
Viscomi, B. V., and Ayre, R. S., 1971, “Nonlinear Dynamic Response of Elastic Slider-Crank Mechanism,” J. Eng. Ind., 93(1), pp. 251–262. [CrossRef]
Sadler, J. P., and Sandor, G. N., 1973, “A Lumped Parameter Approach to Vibration and Stress Analysis of Elastic Linkages,” J. Eng. Ind., 95(2), pp. 549–557. [CrossRef]
Jou, C.-H., 1992, “Dynamic Stability of a High-Speed Slider-Crank Mechanism With a Flexible Connecting Rod,” M.S. thesis, Chung Yuan Christian University, Taiwan.
Fung, R.-F., 1996, “Dynamic Analysis of the Flexible Connecting Rod of a Slider-Crank Mechanism,” ASME J. Vibr. Acoust., 118(4), pp. 687–689. [CrossRef]
Fung, R.-F., 1997, “Dynamic Responses of the Flexible Connecting Rod of a Slider-Crank Mechanism With Time-Dependent Boundary Effect,” Comput. Struct., 63(1), pp. 79–90. [CrossRef]
Irwin, G. R., 1957, “Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate,” ASME J. Appl. Mech., 24(3), pp. 361–364.
Rice, J. R., and Levy, N., 1972, “The Part-Through Surface Crack in an Elastic Plate,” ASME J. Appl. Mech., 39(1), pp. 185–194. [CrossRef]
Dimarogonas, A. D., 1976, Vibration Engineering, West Publishing Co., St. Paul, MN.
Dimarogonas, A. D., and Paipetis, S. A., 1983, Analytical Methods in Rotor Dynamics, Elsevier Applied Science, London, pp. 144–193.
Dimarogonas, A. D., and Massouros, G., 1981, “Torsional Vibration of a Shaft With a Circumferential Crack,” Eng. Fract. Mech., 15(3–4), pp. 439–444. [CrossRef]
Rubio, L., and Fernández-Sáez, J., 2010, “A Note on the Use of Approximate Solutions for the Bending Vibrations of Simply Supported Cracked Beams,” ASME J. Vibr. Acoust., 132(2), p. 024504. [CrossRef]
Mayes, I. W., and Davies, W. G. R., 1984, “Analysis of the Response of a Multi-Rotor-Bearing System Containing a Transverse Crack in a Rotor,” ASME J. Vib., Acoust., 106(1), pp. 139–145. [CrossRef]
Rubio, L., 2009, “An Efficient Method for Crack Identification in Simply Supported Euler–Bernoulli Beams,” ASME J. Vibr. Acoust., 131(5), p. 051001. [CrossRef]
Chondros, T. G., Dimarogonas, A. D., and Yao, J., 2001, “Vibration of a Beam With a Breathing Crack,” J. Sound Vib., 239(1), pp. 57–67. [CrossRef]
Chatterjee, A., 2011, “Nonlinear Dynamics and Damage Assessment of a Cantilever Beam With Breathing Edge Crack,” ASME J. Vibr. Acoust., 133(5), p. 051004. [CrossRef]
Cheng, S. M., Wu, X. J., Wallace, W., and Swamidas, A. S. J., 1999, “Vibrational Response of a Beam With a Breathing Crack,” J. Sound Vib., 225(1), pp. 201–208. [CrossRef]
Dym, C. L., and Shames, I. H., 1973, Solid Mechanics: A Variational Approach, McGraw-Hill, New York, Chap. 4.
Badlani, M., and Midha, A., 1982, “Member Initial Curvature Effects on the Elastic Slider-Crank Mechanism Response,” ASME J. Mech. Des., 104(1), pp. 159–167. [CrossRef]
Papadopoulos, C. A., and Dimarogonas, A. D., 1988, “Coupled Longitudinal and Bending Vibration of a Cracked Shaft,” ASME J. Vib., Acoust., 110(1), pp. 1–8. [CrossRef]
Chondros, T. G., Dimarogonas, A. D., and Yao, J., 1998, “A Continuous Cracked Beam Vibration Theory,” J. Sound Vib., 215(1), pp. 17–34. [CrossRef]
Tada, H., Paris, P. C., and Irwin, G. R., 1985, The Stress Analysis of Cracks Handbook, 2nd ed., Paris Productions Inc., St. Louis, MO.
Rao, S. S., 2004, Mechanical Vibrations, 4th ed., Prentice Hall, Englewood Cliffs, NJ, pp. 588–645.
Clough, R. W., and Penzien, J., 1993, Dynamics of Structures, 2nd ed., McGraw-Hill, New York, pp. 140–165.


Grahic Jump Location
Fig. 3

Slider-crank mechanism with a flexible cracked (x = l/2) connecting rod under deformed configuration

Grahic Jump Location
Fig. 2

Geometry of the rectangular cross-section with straight edge crack

Grahic Jump Location
Fig. 1

Slider-crank mechanism with a flexible cracked (x = l/2) connecting rod under undeformed configuration

Grahic Jump Location
Fig. 4

The dimensionless transverse natural frequency ratio versus the crack depth ratio and comparison with Chondros et al. [16,22]

Grahic Jump Location
Fig. 5

Transient transverse amplitudes of the first and second modes compared with those of Fung [7]

Grahic Jump Location
Fig. 6

Transient transverse amplitude of the second mode g2(τ) compared with that of Jou [5]

Grahic Jump Location
Fig. 7

Comparison among the uncracked, open, and breathing crack models of transverse amplitude g1(τ) at Ω = 0.2266

Grahic Jump Location
Fig. 8

Comparison among the uncracked, open, and breathing crack models of transverse amplitude g2(τ) at Ω = 0.2266

Grahic Jump Location
Fig. 9

Transient transverse amplitude g1(τ) for the breathing crack model with different crack depth ratios at Ω = 0.2

Grahic Jump Location
Fig. 10

Transient transverse amplitude g2(τ) for the breathing crack model with different crack depth ratios at Ω = 0.2



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