Vibrations of clamped orthotropic rectangular plates

Sakata, Toshiyuki; Hosokawa, Kenji

doi:10.1016/0022-460x(88)90252-0

Cited by 33 publications

(19 citation statements)

References 20 publications

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“…In Table IV, comparison studies are carried out for rectangular plates with four combinations of simply supported, clamped and free edges. It is shown that DQFEM solutions agree very closely with the Kantorovich solutions [88] for CSCS and FSFS plates, with the double trigonometric series solution [89] for CCCC plate, even to all available significant digits, and with FEM results for FFFF plate to four significant digits, this implies that the DQFEM precision is independent of boundary conditions. Table V presents comparison studies of five triangular plates with five combinations of simply supported, clamped and free edges, and one corner-supported triangular plate.…”

Section: Numerical Comparisonsmentioning

confidence: 49%

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

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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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Section: Numerical Comparisonsmentioning

confidence: 49%

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

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“…The dynamic behavior of thin plates has been investigated by many researchers [3,4,6,7,13,14,16,17,30,33,36,38,39]. There are also many references on the behavior of the thick plates subjected to different loads.…”

Section: Introductionmentioning

confidence: 99%

Parametric Earthquake Analysis of Thick Plates Using Mindlin’s Theory

Özdemir

Ayvaz

2010

Shock and Vibration

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Abstract. The purpose of this paper is to study parametric earthquake analysis of thick plates using Mindlin's theory, to determine the effects of the thickness/span ratio, the aspect ratio and the boundary conditions on the linear responses of thick plates subjected to earthquake excitations and to present the frequency parameters and the mode shapes of the same plates. In the analysis, finite element method is used for spatial integration and the Newmark-β method is used for time integration. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. In the analysis, 8-noded finite element is used. Graphs and tables are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio. It is also concluded that the effects of the change in the thickness/span ratio on the frequency parameter of the thick plates are always larger than those of the change in the aspect ratio.

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“…Compared to the Rayleigh-Ritz method, the superposition technique in [4] and [5] allows one to obtain an analytical form of the solution which satisfies the governing differential equation and the boundary conditions. Sakata and Hosokawa [6] studied the forced and free vibration of clamped orthotropic plates by using a double trigonometric series. During the last forty years the free vibrations of rectangular plates were studied intensively (see for instance [4]- [9], and the references in those papers).…”

Section: Introductionmentioning

confidence: 99%