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Shock and Vibration
Volume 11, Issue 2, Pages 119-128

Vibration Analysis of Rectangular Plates with Free Corners Using Spline-Based Differential Quadrature

Hongzhi Zhong and Qiang Guo

Department of Civil Engineering, Tsinghua University, Beijing 100084, China

Received 7 May 2003; Accepted 24 September 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A spline-based differential quadrature method (SDQM) is elaborated and applied to the vibration analysis of rectangular plates with free edges. The sextic B-spline functions are used to construct the pertaining cardinal spline interpolants. Thus, explicit expressions of weighting coefficients for approximation of derivatives are obtained. Free vibrations of rectangular plates with free edges, which pose considerable challenge to the conventional differential quadrature, are dealt with and the results are in excellent agreement with those in the literature, highlighting the effectiveness and potential of the spline-based differential quadrature.