Vibration Analysis of Plates With Curvilinear Quadrilateral Planforms by DQM Using Blending Functions

Malik, M.; Bert, Charles W.

doi:10.1006/jsvi.1999.2584

Cited by 25 publications

(10 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A symmetric trapezoidal plate. cubic serendipity interpolations exhibit some convergence and accuracy problems [23]. Apparently, both quartic and cubic serendipity functions embedded in the DQFEM exhibit better convergence than the blending-function and the cubic serendipity function in the DQM.…”

Section: Numerical Comparisonsmentioning

confidence: 98%

“…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.…”

mentioning

confidence: 99%

See 1 more Smart Citation

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

134

View full text Add to dashboard Cite

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.

show abstract

Section: Numerical Comparisonsmentioning

confidence: 98%

mentioning

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

134

View full text Add to dashboard Cite

show abstract

“…The mapping technique can be used to develop irregular elements. It results in the DQEM [1,17,18]. The GDQ can also be used to develop the irregular elements.…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, problems with arbitrary domain configuration can be solved. The DQM has also been used to solve certain problems with specific curve boundaries [17,18].…”

Section: Introductionmentioning

confidence: 99%

DQEM analysis of in-plane vibration of curved beam structures

Chen

2005

Advances in Engineering Software

View full text Add to dashboard Cite

“…The "rst two of these were actually references [35, 36] in reference [1]. It is interesting to note that in reference [2] the sectorial plate planform was more general than that considered in references [1,3,4], because the centers of curvature of the inside and outside curved boundaries were permitted to be di!erent.The present writers acknowledge that the work of reference [1] extended that of reference [2}4] in that the former considered shear deformable (Mindlin) plates rather than thin plates. …”

mentioning

confidence: 99%

Comments on “Differential Quadrature Method for Vibration Analysis of Shear Deformable Annular Sector Plates”

Bert

Malik

2001

Journal of Sound and Vibration

Self Cite

View full text Add to dashboard Cite

Vibration Analysis of Plates With Curvilinear Quadrilateral Planforms by DQM Using Blending Functions

Cited by 25 publications

References 11 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

DQEM analysis of in-plane vibration of curved beam structures

Comments on “Differential Quadrature Method for Vibration Analysis of Shear Deformable Annular Sector Plates”

Contact Info

Product

Resources

About