TECHNICAL PAPERS
Apr 23, 2009

Fatigue Reliability of Multidimensional Vibratory Degrading Systems under Random Loading

Publication: Journal of Engineering Mechanics
Volume 136, Issue 2

Abstract

In this paper, the basic methodology for the fatigue reliability assessment of randomly vibrating multidegree-of-freedom systems is presented within the coupled response-degradation model. The fatigue process in the system components is quantified by the fatigue crack growth equations which—via the stress range—are coupled with the system response. Simultaneously, the system dynamics is affected by fatigue process via its stiffness degradation so that it provides the actual stress values to the fatigue growth equation. In addition to the general coupled response-degradation analysis, its special case of noncoupled fatigue crack growth is treated as well for the wide-band stationary applied stress by the use of its first four spectral moments and the approximate, empirically motivated, Dirlik’s probability distribution for the stress range. Both, the general analysis and the illustrating exemplary problems elaborated in the paper provide the route to the fatigue reliability estimation in complex–hierarchical vibratory systems under random loading.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

This research was cofunded 75% from the European Union (European Social Fund), 25% from the Greek Ministry of Development (General Secretariat of Research and Technology), and from the private sector, in the context of measure 8.3 of the Operational Program Competitiveness (3rd Community Support Framework Program) under Grant No. 03-ΕΔ-524 (PENED 2003). This research was also partially funded by the Ministry of Science of the Republic of Poland. These supports are gratefully acknowledged.UNSPECIFIED

References

Benasciutti, D., and Tovo, R. (2005). “Spectral methods for lifetime prediction under wide-band stationary random processes.” Int. J. Fatigue, 27, 867–877.
Bishop, N. N. M., and Sherrat, F. (1990). “A theoretical solution for the estimation of the rainflow ranges from power spectral density data.” Fatigue Fract. Eng. Mater. Struct., 13(4), 311–326.
Cramer, H., and Leadbetter, M. R. (1967). Stationary and related stochastic processes, Willey, New York.
Dirlik, T. (1985). “Applications of computers to fatigue analysis.” Ph.D. thesis, Warwick Univ.
Gaidai, O., Naess, A., and Sobczyk, K. (2008). “The effect of fatigue-induced crack propagation on the stochastic dynamics of a nonlinear structure.” Probab. Eng. Mech., 23, 438–443.
Gear, C. W. (1971). Numerical initial value problems in ordinary differential, Prentice-Hall, Englewood Cliffs, N.J.
Grigoriu, M. (1990). “Reliability of degrading systems.” Struct. Safety, 8, 345–351.
Igusa, T., and Der Kiureghian, A. (1988). “Response of uncertain systems to stochastic excitations.” J. Eng. Mech., 114, 812–832.
Kotulski, Z., and Sobczyk, K. (1987). “Effects of parameter uncertainty on the response of vibratory systems to random excitations.” J. Sound Vibrat., 119, 159–171.
Lin, Y. K., and Cai, G. Q. (1995). Advanced probabilistic dynamics, McGraw-Hill, New York.
Lutes, L. D., and Sarkani, S. (2003). Random vibrations: Analysis of structural and mechanical systems, Butterworth-Heinemann, Stoneham, Mass.
Miannay, D. P. (1998). Fracture mechanics, Springer, New York.
Papalukopoulos, C., and Natsiavas, S. (2007). “Dynamics of large scale mechanical models using multilevel substructuring.” J. Comput. Nonlinear Dyn., 2(1), 40–51.
Roberts, J. B. (1978). “The response of an oscillator with bilinear hysteresis to stationary random excitation.” ASME J. Appl. Mech., 45, 923–928.
Schueller, G. I. (2007). “On procedures for reliability assessment of mechanical systems and structures.” Struct. Eng. Mech., 25(3), 275–289.
Sobczyk, K. (1991). Stochastic differential equations with applications to physics and engineering, Kluwer Academic, Dodrecht, Boston.
Sobczyk, K., and Spencer, B. F. (1992). Random fatigue: From data to theory, Academic, Boston, San Diego.
Sobczyk, K., and Trebicki, J. (1999). “Stochastic response of degrading stochastic systems.” Proc. IUTAM Symp., rheology of bodies with defects, R. Wang, eds., Kluwer Academic, Dodrecht, Boston.
Sobczyk, K., and Trebicki, J. (2000). “Stochastic dynamics with fatigue induced stiffness degradation.” Probab. Eng. Mech., 15, 91–99.
Soong, T. T., and Grigoriu, M. (1993). Random vibrations of structural and mechanical systems, Prentice-Hall, Englewood Cliffs, N.J.
Wang, X., and Sun, J. Q. (2005). “Multi-stage regression fatigue analysis of non-Gaussian stress processes.” J. Sound Vibrat., 280, 455–465.
Wen, Y. K. (1986). “Stochastic response and damage analysis of inelastic structures.” Probab. Eng. Mech., 1, 57–69.

Information & Authors

Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 136Issue 2February 2010
Pages: 179 - 188

History

Received: Oct 17, 2008
Accepted: Apr 17, 2009
Published online: Apr 23, 2009
Published in print: Feb 2010

Permissions

Request permissions for this article.

Authors

Affiliations

Kazimierz Sobczyk [email protected]
Professor, Dept. of Dynamics of Complex Systems, Institute of Fundamental Technological Research, Polish Academy of Sciences, 21 Swietokrzyska St., 00-049 Warsaw, Poland; and, Department of Mathematics, Informatics and Mechanics, Univ. of Warsaw, Poland (corresponding author). E-mail: [email protected]
Kyriakos Perros
Graduate Student, Dept. of Mechanical and Industrial Engineering, Univ. of Thessaly, Volos 38334, Greece.
Costas Papadimitriou
Professor, Dept. of Mechanical and Industrial Engineering, Univ. of Thessaly, Volos 38334, Greece.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share