Two-dimensional viscoelastic vibration by analytic Fourier p-elements

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

10 Scopus Citations
View graph of relations

Author(s)

  • A. Y T Leung
  • B. Zhu
  • J. Zheng
  • H. Yang

Detail(s)

Original languageEnglish
Pages (from-to)1159-1170
Journal / PublicationThin-Walled Structures
Volume41
Issue number12
Publication statusPublished - Dec 2003

Abstract

Three new Fourier p-elements of rectangular, skew and trapezoidal shapes are given analytically for plane viscoelastic vibration problems. The natural frequencies of the plane viscoelastic structures with complex Young's modulus are computed by a complex eigenvalue solver. With the additional Fourier degrees of freedom, the accuracy of the computed natural frequencies is greatly increased. Since trigonometric functions are used as enriching functions instead of polynomials in the proposal elements, the ill-conditioning problems associated with polynomials of higher degree in the traditional p-version finite element method are avoided. The two mapped plane coordinates in the Jacobian are uncoupled for trapezoidal elements whose element matrices can then be integrated analytically. A triangle can easily be divided into three trapezoids. Therefore, any plane viscoelastic problem with polygonal shape can be analyzed by a combination of rectangular and trapezoidal elements. Numerical examples show that the convergence of the present elements is very fast with respect to the number of trigonometric terms. The natural frequencies of several polygonal viscoelastic plates subject to in-plane vibration are presented. © 2003 Elsevier Ltd. All rights reserved.

Research Area(s)

  • Analytic integration, Complex modulus, Fourier p-element, Plane problem, Viscoelastic vibration

Citation Format(s)

Two-dimensional viscoelastic vibration by analytic Fourier p-elements. / Leung, A. Y T; Zhu, B.; Zheng, J.; Yang, H.

In: Thin-Walled Structures, Vol. 41, No. 12, 12.2003, p. 1159-1170.

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