The efficient nonlinear vibration analysis of a rotating elastic structure with a crack is examined. In particular, the solution of the forced vibration response of a cracked turbine engine blade is investigated. Starting with a finite element model of the cracked system, the Craig–Bampton method of component mode synthesis is used to generate a reduced-order model that retains the nodes of the crack surfaces as physical degrees of freedom. The nonlinearity due to the intermittent contact of the crack surfaces, which is caused by the opening and closing of the crack during each vibration cycle, is modeled with a piecewise linear term in the equations of motion. Then, the efficient solution procedure for solving the resulting nonlinear equations of motion is presented. The approach employed in this study is a multiharmonic hybrid frequency∕time-domain technique, which is an extension of the traditional harmonic balance method. First, a simple beam model is used to perform a numerical validation by comparing the results of the new method to those from transient finite element analysis (FEA) with contact elements. It is found that the new method retains good accuracy relative to FEA while reducing the computational costs by several orders of magnitude. Second, a representative blade model is used to examine the effects of crack length and rotation speed on the resonant frequency response. Several issues related to the rotation are investigated, including geometry changes of the crack, shifts in resonant frequencies, and the existence of multiple solutions. For the cases considered, it is found that the nonlinear vibration response exhibits the jump phenomenon only when rotation is included in the model.
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e-mail: asakira@umich.edu
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January 2009
Research Papers
Efficient Nonlinear Vibration Analysis of the Forced Response of Rotating Cracked Blades
Akira Saito,
Akira Saito
Student
Mem. ASME
Department of Mechanical Engineering,
e-mail: asakira@umich.edu
University of Michigan
, Ann Arbor, MI 48109-2125
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Matthew P. Castanier,
Matthew P. Castanier
Mem. ASME
Department of Mechanical Engineering,
e-mail: mpc@umich.edu
University of Michigan
, Ann Arbor, MI 48109-2125
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Christophe Pierre,
Christophe Pierre
Fellow ASME
Faculty of Engineering,
e-mail: christophe.pierre@mcgill.ca
McGill University
, Montreal QC, H3A 2K6, Canada
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Olivier Poudou
Olivier Poudou
Department of Mechanical Engineering,
University of Michigan
, Ann Arbor, MI 48109-2125 olivier.poudou@ge.com.poudou@umich.edu
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Akira Saito
Student
Mem. ASME
Department of Mechanical Engineering,
University of Michigan
, Ann Arbor, MI 48109-2125e-mail: asakira@umich.edu
Matthew P. Castanier
Mem. ASME
Department of Mechanical Engineering,
University of Michigan
, Ann Arbor, MI 48109-2125e-mail: mpc@umich.edu
Christophe Pierre
Fellow ASME
Faculty of Engineering,
McGill University
, Montreal QC, H3A 2K6, Canadae-mail: christophe.pierre@mcgill.ca
Olivier Poudou
Department of Mechanical Engineering,
University of Michigan
, Ann Arbor, MI 48109-2125 olivier.poudou@ge.com.poudou@umich.eduJ. Comput. Nonlinear Dynam. Jan 2009, 4(1): 011005 (10 pages)
Published Online: November 11, 2008
Article history
Received:
August 8, 2007
Revised:
July 2, 2008
Published:
November 11, 2008
Citation
Saito, A., Castanier, M. P., Pierre, C., and Poudou, O. (November 11, 2008). "Efficient Nonlinear Vibration Analysis of the Forced Response of Rotating Cracked Blades." ASME. J. Comput. Nonlinear Dynam. January 2009; 4(1): 011005. https://doi.org/10.1115/1.3007908
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