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# Extension of Rayleigh–Ritz method for eigenvalue problems with discontinuous boundary conditions applied to vibration of rectangular plates

Gavalas, George R. and El-Raheb, Michael (2014) Extension of Rayleigh–Ritz method for eigenvalue problems with discontinuous boundary conditions applied to vibration of rectangular plates. Journal of Sound and Vibration, 333 (17). pp. 4007-4016. ISSN 0022-460X. https://resolver.caltech.edu/CaltechAUTHORS:20140725-075706960

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## Abstract

The Rayleigh–Ritz (R–R) method is extended to eigenvalue problems of rectangular plates with discontinuous boundary conditions (DBC). Coordinate functions are defined as sums of products of orthogonal polynomials and consist of two parts, each satisfying the BC in its respective region. These parts are matched by minimizing the mean square error of functions and their x-derivatives at the interface between regions. Matching defines a positive definite 2N^2 × 2N^2 matrix Q whose eigenvectors form the orthogonal coordinate functions. The corresponding eigenvalues measure the matching error of the two parts at the interface. When applying the R–R method, the total error is the sum of the matching error and that arising from the finite number of coordinate functions. Although most of the coordinate functions correspond to the zero eigenvalue, these do not suffice and additional functions corresponding to small but finite eigenvalues must be included. In three examples with discontinuous BC of the clamped, simply supported and free kind, the calculated frequencies match closely those from a finely discretized finite element method.

Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.jsv.2014.03.030 DOIArticle
http://www.sciencedirect.com/science/article/pii/S0022460X14002314PublisherArticle
ORCID:
AuthorORCID
Gavalas, George R.0000-0003-1468-6835
Additional Information:© 2014 Elsevier Ltd. Received 10 May 2013; Received in revised form 21 March 2014; Accepted 24 March 2014. Handling Editor: H. Ouyang. Available online 10 May 2014.
Issue or Number:17
Record Number:CaltechAUTHORS:20140725-075706960
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140725-075706960
Official Citation:George R. Gavalas, Michael El-Raheb, Extension of Rayleigh–Ritz method for eigenvalue problems with discontinuous boundary conditions applied to vibration of rectangular plates, Journal of Sound and Vibration, Volume 333, Issue 17, 18 August 2014, Pages 4007-4016, ISSN 0022-460X, http://dx.doi.org/10.1016/j.jsv.2014.03.030. (http://www.sciencedirect.com/science/article/pii/S0022460X14002314)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:47490
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:25 Jul 2014 15:58