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AuthorBahaloo, Hassan
AuthorPapadopolus, Jim
AuthorGhosh, Ranajay
AuthorMahdi, Elsadig
AuthorVaziri, Ashkan
AuthorNayeb-Hashemi, Hamid
Available date2021-09-01T10:02:48Z
Publication Date2016
Publication NameInternational Journal of Mechanical Sciences
ResourceScopus
URIhttp://dx.doi.org/10.1016/j.ijmecsci.2016.03.004
URIhttp://hdl.handle.net/10576/22410
AbstractOut of plane vibration of rotating disks limits their performances especially at certain critical speed. The critical speed of these disks may be affected by the presence of defects such as a circumferential crack. In this paper out of plane vibration of functionally graded (FG) rotating annular disks with a circumferential open crack is investigated. The cracked disk is modeled as two sub-disks, connected at the crack location by translational and rotational line springs, simulating the crack plate response to induced shear force and bending moment at the crack radius. These spring stiffness constants are obtained numerically using the finite element method (FEM) as a function of crack depth and radius. The rotational spring stiffness strongly depends on the disk rotation speed, while the stiffness of the translational spring is found to be independent of the disk speed. Both spring constants depend on the spatial distribution of the disk elastic modulus. The in-plane disk stresses are obtained using a semi-analytical approach. Those in plane stresses are used to obtain the governing equation of out of plane motion of the disk. A finite difference scheme is used to solve the partial differential equation of motion to obtain eigenvalues, critical speed and associated mode shapes. The lowest critical speed, which is one of the important parameters limiting the performance of the rotating disk, is obtained from the Campbell Diagram. It is found that irrespective of the distribution of the modulus of elasticity in the FG disk, increasing the crack depth or decreasing the crack radial distance from the disk center decreases the critical speed. The critical speed reduction is more pronounced for the case when the disk material modulus of elasticity is decreasing from the disk center. 2016 Elsevier Ltd. All rights reserved.
SponsorThis work has been supported by the Qatar National Research Foundation (QNRF) under Award no. NPRP 5-068-2-024 .
Languageen
PublisherElsevier Ltd
SubjectCrack propagation
Cracks
Eigenvalues and eigenfunctions
Elastic moduli
Equations of motion
Finite difference method
Finite element method
Speed
Stiffness
Circumferential cracks
Finite difference scheme
Functionally graded
Governing equations
Out-of-plane vibrations
Rotating annular disk
Semi-analytical approaches
Transverse vibrations
Rotating disks
TitleTransverse vibration and stability of a functionally graded rotating annular disk with a circumferential crack
TypeArticle
Pagination26-35
Volume Number113
dc.accessType Abstract Only


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