Harmonic differential quadrature (HDQ) for axisymmetric bending analysis of thin isotropic circular plates

Cívalek, Ömer; Ülker, Mehmet

doi:10.12989/sem.2004.17.1.001

Cited by 87 publications

(26 citation statements)

References 31 publications

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“…Hosseini-Hashemi et al [6] presented the free vibration of functionally graded circular plate with stepped thickness via Mindlin plate theory. By employing harmonic differential quadrature method for obtaining numerical solution of circular plate, Civalek and Uelker [7] made a further analysis for the behavior of the boundary conditions of fixed and simply supported. Moreover, the results obtained by finite difference method were compared with those calculated by harmonic differential quadrature method, whose feasibility is verified by Bakhshi Khaniki and Hosseini-Hashemi [8].…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Rings via Wave Approach

Wang

Liu

Shuai

et al. 2018

Shock and Vibration

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Free vibration of rings is presented via wave approach theoretically. Firstly, based on the solutions of out-of-plane vibration, propagation, reflection, and coordination matrices are derived for the case of a fixed boundary at inner surface and a free boundary at outer surface. Then, assembling these matrices, characteristic equation of natural frequency is obtained. Wave approach is employed to study the free vibration of these ring structures. Natural frequencies calculated by wave approach are compared with those obtained by classical method and Finite Element Method (FEM). Afterwards natural frequencies of four type boundaries are calculated. Transverse vibration transmissibility of rings propagating from outer to inner and from inner to outer is investigated. Finally, the effects of structural and material parameters on free vibration are discussed in detail.

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Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Rings via Wave Approach

Wang

Liu

Shuai

et al. 2018

Shock and Vibration

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“…Detailed results for frequencies of circular plates were listed by Leissa and Narita [27]. Different types of differential quadrature (DQ) methods have been used for vibration analysis of circular plates by Civalek [28,29]. Liewet al [30] analyzed the thick plates on elastic foundations via DQ method.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of annular sector plates via conical shell equations

Demir

Ersoy

Mercan

et al. 2017

Curved and Layered Structures

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Abstract:In this paper, free vibration analysis of annular sector plates has been presented via conical shell equations. By using the first-order shear deformation theory (FSDT) equation of motion of conical shell is obtained. The method of discrete singular convolution (DSC) and method differential quadrature (DQ) are used for solution of the vibration problem of annular plates for some special value of semi-vertex angle via conical shell equation. The obtained numerical results based on the two numerical approaches for annular sector plates compare well with the results available in the literature. The effects of some geometric parameters, grid numbers and types of the grid distribution have been discussed for curved plates.

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“…[48][49][50][51][52][53][54]. It gives highly accurate solution with minimal computational effort not only for plates of various geometries [55][56][57][58][59][60] but even for sectorial plates [61][62][63].…”

Section: Introductionmentioning

confidence: 99%