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Mathematics > Analysis of PDEs

arXiv:1804.10583 (math)
[Submitted on 27 Apr 2018 (v1), last revised 31 Oct 2018 (this version, v2)]

Title:An analytical closed-form solution for free vibration of stepped circular/annular Mindlin functionally graded plate

Authors:Masoud Derakhshani, Shahrokh Hosseini-Hashemi, Mohammad Fadaee
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Abstract:An exact solution based on a unique procedure is presented for free vibration of stepped circular and annular functionally graded (FG) plates via first-order shear deformation plate theory of Mindlin. A power-law distribution of the volume fraction of the components is considered for the Young's Modulus and Poisson's ratio of the studied FG plate. Free vibration of the plate is solved by introducing some new potential functions and the use of separation of variables method. Finally, several comparisons of the developed model were presented with the FEA analysis, to demonstrate the accuracy of the proposed exact procedure. The effect of the geometrical parameters such as step thickness ratios and step locations on the natural frequencies of FG plates is also investigated.
Comments: 11 pages, 3 figures, This paper was presented and published in the 1st International Conference on Acoustic and Vibrations (ISAV 2011)
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1804.10583 [math.AP]
  (or arXiv:1804.10583v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.10583

Submission history

From: Masoud Derakhshani [view email]
[v1] Fri, 27 Apr 2018 16:32:04 UTC (365 KB)
[v2] Wed, 31 Oct 2018 23:19:09 UTC (389 KB)
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