Radial vibration analysis of heterogeneous and non-uniform disks via complementary functions method

Free vibration analysis of heterogeneous (functionally graded) and non-uniform (variable thickness) disks using plane elasticity results in a two-point boundary value problem. Spatially varying mechanical and thickness properties yield variable coefficient governing differential equations where obta...

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Bibliographic Details
Published in:Journal of strain analysis for engineering design 2018-07, Vol.53 (5), p.332-337
Main Authors: Yildirim, Sefa, Tutuncu, Naki
Format: Article
Language:English
Subjects:
Boundary value problems
Differential equations
Disks
Elasticity
Free vibration
Functionally gradient materials
Grading
Resonant frequencies
Variable thickness
Vibration analysis
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Summary:Free vibration analysis of heterogeneous (functionally graded) and non-uniform (variable thickness) disks using plane elasticity results in a two-point boundary value problem. Spatially varying mechanical and thickness properties yield variable coefficient governing differential equations where obtaining closed-form solutions are not possible except for certain simple grading and thickness functions. This article uses complementary functions method as a novel approach to determine natural frequencies of functionally graded non-uniform disks. The validation and observation of converges are done using analytical and ANSYS results for a simple power law model uniform disk. The proposed solution method can be applied for disks with any continuous thickness and material grading functions.
ISSN:0309-3247
2041-3130
DOI:10.1177/0309324718765006