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Journal ArticleDOI

Finite element analysis of three-dimensional vibrations of thick circular and annular plates

25 May 2000-Journal of Sound and Vibration (Academic Press)-Vol. 233, Iss: 1, pp 63-80
TL;DR: In this paper, a finite element method for 3D vibration analysis of annular and circular plates is presented. But the method is different from the traditional 3D finite element analysis and is reduced to a sequence of 2-D analyses one for each circumferential wave number.
About: This article is published in Journal of Sound and Vibration.The article was published on 2000-05-25. It has received 57 citations till now. The article focuses on the topics: Mixed finite element method & Extended finite element method.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the effect of shear deformations using the first-order shear deformation theory is derived and solved exactly for various combinations of boundary conditions by using the exact element method.

299 citations

Journal ArticleDOI
G.J. Nie1, Z. Zhong1
TL;DR: In this article, a semi-analytical method using the state space method and the one-dimensional differential quadrature method is used to obtain the vibration frequencies and dynamic responses of circular plates.

132 citations

Journal ArticleDOI
TL;DR: In this article, the authors present an overview of various semi-analytical numerical methods for quasi-three-dimensional (3D) analyses of laminated composite and multilayered (or sandwiched) functionally graded elastic/piezoelectric materials (FGEMs/FGPMs) plates and shells with combinations of simply-supported, free and clamped edge conditions.

106 citations

Journal ArticleDOI
TL;DR: It is shown that the mass matrices of C0 finite element in DQFEM are diagonal, which can reduce the computational cost for dynamic problems, and the reformulated DQ rules for curvilinear quadrilateral domain and its implementation are presented.
Abstract: This paper studies the differential quadrature finite element method (DQFEM) systematically, as a combination of differential quadrature method (DQM) and standard finite element method (FEM), and formulates one- to three-dimensional (1-D to 3-D) element matrices of DQFEM. It is shown that the mass matrices of C0 finite element in DQFEM are diagonal, which can reduce the computational cost for dynamic problems. The Lagrange polynomials are used as the trial functions for both C0 and C1 differential quadrature finite elements (DQFE) with regular and/or irregular shapes, this unifies the selection of trial functions of FEM. The DQFE matrices are simply computed by algebraic operations of the given weighting coefficient matrices of the differential quadrature (DQ) rules and Gauss-Lobatto quadrature rules, which greatly simplifies the constructions of higher order finite elements. The inter-element compatibility requirements for problems with C1 continuity are implemented through modifying the nodal parameters using DQ rules. The reformulated DQ rules for curvilinear quadrilateral domain and its implementation are also presented due to the requirements of application. Numerical comparison studies of 2-D and 3-D static and dynamic problems demonstrate the high accuracy and rapid convergence of the DQFEM.

84 citations


Cites methods from "Finite element analysis of three-di..."

  • ...DQM has been applied to irregular domains with the help of the27 natural-to-Cartesian geometric mapping using the serendipity-family interpolation functions [Bert and Malik, 1996; Xing and Liu, 2009] or the blending functions29 which permit exact mapping [Malik and Bert, 2000]....

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Journal ArticleDOI
TL;DR: In this article, free axisymmetric vibrations of non-homogeneous isotropic circular plates of nonlinear thickness variation have been analyzed on the basis of classical plate theory employing the DQ method.

58 citations

References
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Journal ArticleDOI
TL;DR: In this article, the Ritz method is applied in a three-dimensional analysis to obtain accurate frequencies for thick circular and annular plates, formulated in a manner which allows one to have any combination of free or fixed plate boundaries.

95 citations

Journal ArticleDOI
TL;DR: In this paper, a method of 3D analysis for the free vibration frequencies and mode shapes of solid circular cylinders of elastic material was developed. But the method assumes for the three displacement components a Fourier series in the circumferential (θ) direction and algebraic polynomials in the radial (r) and axial (z) directions.
Abstract: A method of three‐dimensional (3‐D) analysis is developed for the free vibration frequencies and mode shapes of solid circular cylinders of elastic material. The method assumes for the three displacement components a Fourier series in the circumferential (θ) direction and algebraic polynomials in the radial (r) and axial (z) directions. All types of boundary conditions and arbitrary length‐to‐diameter ratios (L/D) may be accommodated. Extensive convergence studies show that frequencies which are exact to five or six significant figures may be obtained for cylinders with free–free ends, and that three or four figure accuracy is achievable for fixed–free ends. These accurate frequencies are compared with ones determined from known elementary and improved 1‐D theories for longitudinal, torsional, and bending modes for various L/D ratios, thereby establishing the ranges of accuracy of the 1‐D analyses for circular cross sections.

73 citations

Journal ArticleDOI
TL;DR: In this paper, a set of tables for the first five symmetric and first five antisymmetric modes of a hollow or solid cylinder for circumferential wave numbers n = 0, 1, 2 is given.

63 citations

Journal ArticleDOI
TL;DR: In this article, the first known values of frequencies from 3D analysis of cylinders having one end fixed, with all other boundaries free, are also presented in considerable detail, compared with less accurate 3D results published previously by other researchers.
Abstract: A three‐dimensional (3‐D) method of analysis developed in a companion paper [A. W. Leissa and J. So, J. Acoust Soc. Am. 98, 2122–2135 (1995)] is used to obtain free‐vibration frequencies of completely free‐elastic cylinders. Extensive, accurate data are presented for the first 20 frequencies of each circumferential wave number 0–5 for free–free cylinders having length‐to‐diameter ratios (L/D) of 1, 1.5, 2, 3, and 5 with a Poisson’s ratio (ν) of 0.3. An additional study for L/D=1 over the full range (0≤ν<0.5) possible for isotropic materials shows that Poisson’s ratio effects can be quite important. The first known values of frequencies from 3‐D analysis of cylinders having one end fixed, with all other boundaries free, are also presented in considerable detail. For free–free cylinders, comparisons are made with less accurate 3‐D results published previously by other researchers.

63 citations