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research-article

Generalized BAA and X-Xr for Modeling Cyclically Symmetric Structures With Cracks

[+] Author and Article Information
Meng-Hsuan Tien

Department of Mechanical & Aerospace Engineering, The Ohio State University, Columbus, Ohio 43210
tien.36@osu.edu

Tianyi Hu

Department of Mechanical & Aerospace Engineering, The Ohio State University, Columbus, Ohio 43210
hu.629@osu.edu

Kiran X. D'Souza

Department of Mechanical & Aerospace Engineering, The Ohio State University, Columbus, Ohio 43210
dsouza.60@osu.edu

1Corresponding author.

ASME doi:10.1115/1.4039296 History: Received September 07, 2017; Revised February 05, 2018

Abstract

Analysis of the influence of cracks on the dynamics of bladed disks is critical for design, failure prognosis, and structural health monitoring. Predicting the dynamics of cracked bladed disks is computationally challenging for two reasons: (1) the model size is quite large, and (2) the piecewise-linear nonlinearity caused by contact eliminates the use of linear analysis tools. Recently, a technique referred to as the X-Xr approach was developed to efficiently reduce the model size of cracked bladed disks. The method employs relative coordinates to describe the motion of crack surfaces such that an effective model reduction can be achieved using single sector calculations. More recently, a method referred to as the generalized bilinear amplitude approximation (generalized BAA) was developed to approximate the amplitude and frequency of piecewise-linear nonlinear systems. This paper modifies the generalized BAA method and combines it with the X-Xr approach to efficiently predict the dynamics of cracked bladed disks. The combined method is able to construct the reduced-order model of full disks using single-sector models only and estimate the amplitude and frequency with a significantly reduced computational effort. The proposed approach is demonstrated on a three degrees-of-freedom spring-mass system and a cracked bladed disk.

Copyright (c) 2018 by ASME
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