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DSC‐Ritz method for the free vibration analysis of Mindlin plates
Author(s) -
Hou Yunshan,
Wei G. W.,
Xiang Y.
Publication year - 2004
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1186
Subject(s) - ritz method , mathematics , vibration , convolution (computer science) , boundary value problem , convergence (economics) , mathematical analysis , basis function , basis (linear algebra) , geometry , computer science , physics , quantum mechanics , machine learning , artificial neural network , economics , economic growth
This paper introduces a novel method for the free vibration analysis of Mindlin plates. The proposed method takes the advantage of both the local bases of the discrete singular convolution (DSC) algorithm and the pb ‐2 Ritz boundary functions to arrive at a new approach, called DSC‐Ritz method. Two basis functions are constructed by using DSC delta sequence kernels of the positive type. The energy functional of the Mindlin plate is represented by the newly constructed basis functions and is minimized under the Ritz variational principle. Extensive numerical experiments are considered by different combinations of boundary conditions of Mindlin plates of rectangular and triangular shapes. The performance of the proposed method is carefully validated by convergence analysis. The frequency parameters agree very well with those in the literature. Numerical experiments indicate that the proposed DSC‐Ritz method is a very promising new method for vibration analysis of Mindlin plates. Copyright © 2004 John Wiley & Sons, Ltd.