Vibration of skew plates by the MLS-Ritz method

Zhou, Li; Zheng, Wei Xing

doi:10.1016/j.ijmecsci.2008.05.002

Cited by 45 publications

(15 citation statements)

References 33 publications

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“…The title problem or the free vibrations of isotropic thin plates with different planforms have been studied extensively due to a variety of applications by using the FEM [52][53][54][55][56], the Ritz method [57][58][59][60][61][62][63], the DQM [5,23,[64][65][66][67][68][69][70], the discrete singular convolution (DSC) method [71][72][73], the superposition method [74][75][76], the Green function method [77], the moving least-square Ritz method [78] and the Galerkin method [79]. In the above paragraph there are some comments on FEM and DQM.…”

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confidence: 99%

High‐accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain

Xing

Liu

2009

Numerical Meth Engineering

132

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SUMMARYBased on the differential quadrature (DQ) rule, the Gauss Lobatto quadrature rule and the variational principle, a DQ finite element method (DQFEM) is proposed for the free vibration analysis of thin plates. The DQFEM is a highly accurate and rapidly converging approach, and is distinct from the differential quadrature element method (DQEM) and the quadrature element method (QEM) by employing the function values themselves in the trial function for the title problem.The DQFEM, without using shape functions, essentially combines the high accuracy of the differential quadrature method (DQM) with the generality of the standard finite element formulation, and has superior accuracy to the standard FEM and FDM, and superior efficiency to the p-version FEM and QEM in calculating the stiffness and mass matrices.By incorporating the reformulated DQ rules for general curvilinear quadrilaterals domains into the DQFEM, a curvilinear quadrilateral DQ finite plate element is also proposed. The inter-element compatibility conditions as well as multiple boundary conditions can be implemented, simply and conveniently as in FEM, through modifying the nodal parameters when required at boundary grid points using the DQ rules. Thus, the DQFEM is capable of constructing curvilinear quadrilateral elements with any degree of freedom and any order of inter-element compatibilities. A series of frequency comparisons of thin isotropic plates with irregular and regular planforms validate the performance of the DQFEM.

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confidence: 99%

High‐accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain

Xing

Liu

2009

Numerical Meth Engineering

132

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“…Using least-square-based on finite difference method, Shu et al (2007) studied free vibration analysis of plates. Using moving least square Ritz method, Zhou and Zheng (2008) presented a numerical solution for vibration analysis of skew plates. Shufrin et al (2010) presented a semi-analytical solution for the geometrically nonlinear analysis of skew and trapezoidal plates subjected to out-of-plane loads.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of a cantilevered trapezoidal moderately thick plate with variable thickness

Torabi¹,

Afshari²

2017

10.5267/j.esm

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This paper presents a numerical solution for vibration analysis of cantilevered non-uniform trapezoidal thick plates. Based on the first shear deformation theory, kinetic and strain energies of the plate are derived and using Hamilton's principle, governing equations and boundary conditions are derived. A transformation of coordinates is used to convert the equations and boundary conditions from the original coordinates into a new computational coordinates. Using Differential quadrature method (DQM), natural frequencies and corresponding modes are derived numerically. Convergence and accuracy of the proposed solution are confirmed using results presented by other authors and also results obtained based on the finite element method using ANSYS software. Finally, as the case studies, two cases for variation of thickness are considered and the effects of angles, aspect ratio and thickness of the plate on the natural frequencies are studied. It is concluded that two angles of the trapezoid have opposite effect on the natural frequencies. Also, it is shown that all frequencies rise as value of thickness increases or value of the aspect ratio of the plate decreases. The most advantage of the proposed solution is its applicability for plates with variable thickness.

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“…Woo et al 16 determined natural frequencies and mode shapes of a skew Mindlin plate using P-version of the finite element method under different sets of boundary conditions and discussed the effect of skew angle, aspect ratio, and cutout dimension on the frequency parameter. Zhou and Zheng 17 came out with accurate results on vibration of skew plate by utilizing moving least square -Ritz method. Results, thus obtained, were found close to the available results in literature but certain mode frequencies deviated from the data presented by Mc Gee et al, 12 Hung et al, 13 and Mc Gee et al 15 Mizusawa and Kondo 18 investigated vibration of the skew plate with linearly varied thickness along longitudinal axis by using the spline spring method.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Rhombic Plate with Central Crack

Azam¹,

Ranjan²,

Kumar³

2017

IJAV

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In this paper, free vibration analysis of rhombic plate with pre-existing central crack has been done using the finite element method. The Mindlin theory of plate has been used in the process of investigation. The following six boundary conditions at the edges of the plate have been considered. They are simply supported at all edges (SSSS), clamped at all edges (CCCC), free at all edges (FFFF), clamped-simply supported (CSSC), clamped-free (CFFC), and clamped-free-simply supported (CSFS). Effects of crack length on natural frequencies of rhombic plate with different skew angles i.e. 15• , 30• , 45• , 60• have been studied. It is observed that percentage drop in fundamental frequency due to presence of central crack in the rhombic plate increases with an increase in skew angle for CCCC, SSSS, and CSSC edge conditions at a given crack ratio (non-dimensional crack length). Under the CFFC, CSFS, and FFFF edge conditions, percentage drop in natural frequency of rhombic plate is very small for crack ratio of 0.2 at different skew angles. In case of the CFFC edge condition of the rhombic plate, percentage drop in fundamental frequency is within 0.7% at all skew angles and with all crack ratios considered. Some of the results obtained by the present method have been compared with the published results. Most of the results obtained are novel for rhombic crack plate.

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Vibration of skew plates by the MLS-Ritz method

Cited by 45 publications

References 33 publications

High‐accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain

High‐accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain

Vibration analysis of a cantilevered trapezoidal moderately thick plate with variable thickness

Free Vibration Analysis of Rhombic Plate with Central Crack

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