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Statistical Analysis of the Nonlinear Response of Bladed Disks with Mistuning and Cracks

Meng-Hsuan Tien

The Ohio State University, Columbus, Ohio 43210

*Fast Fellow, Department of Mechanical and Aerospace Engineering; .

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Tianyi Hu

The Ohio State University, Columbus, Ohio 43210

†Graduate Student, Department of Mechanical and Aerospace Engineering; .

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and

Kiran D’Souza

The Ohio State University, Columbus, Ohio 43210

‡Assistant Professor, Department of Mechanical and Aerospace Engineering; (Corresponding Author).

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Published Online:3 Jul 2019https://doi.org/10.2514/1.J058190

Abstract

In this paper, efficient techniques are presented for analyzing the dynamics of mistuned bladed disks with cracks. The analysis of the influence of cracks, coupled with the influence of mistuning on the dynamics of bladed disks, is computationally challenging for several reasons: 1) complex geometry of modern turbines results in very high-dimensional computational models; 2) mistuning in these structures breaks the cyclic symmetry in these systems; and 3) cracks further disrupt the symmetry and introduce a piecewise-linear nonlinearity into these systems. Recently, several approaches have been developed to handle these challenges individually. The component mode mistuning approach was developed to efficiently model small mistuning in bladed disks. The $X - X_{r}$ method was developed for generating reduced-order models of cyclically symmetric systems with cracks. More recently, the generalized bilinear amplitude approximation technique was created to efficiently approximate the nonlinear vibrational response of a class of piecewise-linear nonlinear systems. This paper modifies and combines these techniques, for the first time, to enable efficient modeling and statistical analysis of bladed disks with mistuning and cracks. The novel method is able to generate the reduced-order model of full-bladed disks using only single-sector models and approximate the nonlinear vibrational response of the system with significantly reduced computational effort. A high-dimensional finite element model of a mistuned bladed disk with a crack is studied using the proposed approach. The influence of mistuning patterns and cracks on the vibrational response of the bladed disk is discussed.

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Volume 57, Number 11November 2019

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Copyright © 2019 by Meng-Hsuan Tien, Tianyi Hu, and Kiran D’Souza. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. All requests for copying and permission to reprint should be submitted to CCC at www.copyright.com; employ the eISSN 1533-385X to initiate your request. See also AIAA Rights and Permissions www.aiaa.org/randp.

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Acknowledgments

This paper is based on work partially supported by the National Science Foundation under Grant No. 1902408, program manager Robert Landers. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors would also like to acknowledge the financial support from the Future Academic Scholars Training program of the Department of Mechanical and Aerospace Engineering at The Ohio State University.

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Received20 December 2018
Accepted20 May 2019
Published online3 July 2019

Statistical Analysis of the Nonlinear Response of Bladed Disks with Mistuning and Cracks

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