A trapezoidal Fourier p-element for membrane vibrations

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Author(s)

  • A. Y T Leung
  • Bin Zhu
  • Jianjin Zheng
  • Hao Yang

Detail(s)

Original languageEnglish
Pages (from-to)479-491
Journal / PublicationThin-Walled Structures
Volume41
Issue number5
Publication statusPublished - May 2003

Abstract

A trapezoidal Fourier p-element for the analysis of membrane transverse vibrations is investigated. Trigonometric functions are used as shape functions instead of polynomials to avoid ill-conditioning problems. The element matrices are analytically integrated in closed form. With the enrichment degrees of freedom in Fourier series, the accuracy of natural frequencies obtained is increased in a stable manner. One element can predict many modes accurately. Since a triangle can be divided into three trapezoidal elements, the range of application is wider than the previously derived rectangular Fourier p-element. The natural modes of a square membrane consisting of two trapezoidal elements are computed as test cases and convergence is very fast with an increasing number of trigonometric terms. Comparison of natural modes calculated by the trapezoidal Fourier p-element and the conventional finite elements is carried out. The results show that the trapezoidal Fourier p-element produces higher accurate natural frequencies than the conventional finite elements with the same number of degrees of freedom. © 2003 Elsevier Science Ltd. All rights reserved.

Research Area(s)

  • Fourier p-element, Membrane, Trapezoidal element, Vibration

Citation Format(s)

A trapezoidal Fourier p-element for membrane vibrations. / Leung, A. Y T; Zhu, Bin; Zheng, Jianjin; Yang, Hao.

In: Thin-Walled Structures, Vol. 41, No. 5, 05.2003, p. 479-491.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal