Free vibration and bending analysis of circular Mindlin plates using singular convolution method

Cívalek, Ömer; Ersoy, Hakan

doi:10.1002/cnm.1138

Cited by 17 publications

(5 citation statements)

References 80 publications

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“…Mindlin [8] presented the moderate thickness plate theory in which, the shear effect that was ignored in the classical thin plate theory was considered by introducing a shear correction factor. Civalek [9] and Civalek and Eesoy [10] used the singular convolution method to study the free vibration of annular sector plates and circular Mindlin plates, respectively. Zhong and Yu [11] studied the free vibration of an eccentric annular Mindlin plate by using the weak-form quadrature element.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional vibrations of annular thick plates with linearly varying thickness

Zhou

2011

Arch Appl Mech

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The free vibration of annular thick plates with linearly varying thickness along the radial direction is studied, based on the linear, small strain, three-dimensional (3-D) elasticity theory. Various boundary conditions, symmetrically and asymmetrically linear variations of upper and lower surfaces are considered in the analysis. The well-known Ritz method is used to derive the eigen-value equation. The trigonometric functions in the circumferential direction, the Chebyshev polynomials in the thickness direction, and the Chebyshev polynomials multiplied by the boundary functions in the radial direction are chosen as the trial functions. The present analysis includes full vibration modes, e.g., flexural, thickness-shear, extensive, and torsional. The first eight frequency parameters accurate to at least four significant figures for five vibration categories are obtained. Comparisons of present results for plates having symmetrically linearly varying thickness are made with others based on 2-D classical thin plate theory, 2-D moderate thickness plate theory, and 3-D elasticity theory. The first 35 natural frequencies for plates with asymmetrically linearly varying thickness are compared to the finite element solutions; excellent agreement has been achieved. The asymmetry effect of upper and lower surface variations on the frequency parameters of annular plates is discussed in detail. The first four modes of axisymmetric vibration for completely free circular plates with symmetrically and asymmetrically linearly varying thickness are plotted. The present results for 3-D vibration of annular plates with linearly varying thickness can be taken as benchmark data for validating results from various plate theories and numerical methods.

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Section: Introductionmentioning

confidence: 99%

Three-dimensional vibrations of annular thick plates with linearly varying thickness

Zhou

2011

Arch Appl Mech

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“…us, the research on the mechanical behavior of orthotropic plate aroused the interest of scientists and engineers for more than a century. Literature surveys reveal that numerical methods such as finite difference method [1], spline element method [2], boundary element method [3], meshless method [4], finite element method (FEM) [5], boundary particle method [6], isogeometric collocation method [7], discrete singular convolution method [8][9][10][11], and differential quadrature method [12,13] are competent to analyze the bending of plates with different edge conditions, loading patterns, and material properties. However, the aforementioned numerical methods satisfy the engineering requirements with acceptable error, but approximate solution is obtained, which is the main disadvantage of the numerical methods.…”

Section: Introductionmentioning

confidence: 99%

Analytical Bending Solutions of Orthotropic Rectangular Thin Plates with Two Adjacent Edges Free and the Others Clamped or Simply Supported Using Finite Integral Transform Method

Zhong

Ullah

et al. 2020

Advances in Civil Engineering

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For the first time, the finite integral transform method is introduced to explore the accurate bending analysis of orthotropic rectangular thin plates with two adjacent edges free and the others clamped or simply supported. Previous solutions mostly focused on plates with simply supported and clamped edges, but the existence of free corner makes the solution procedure much complex to solve by conventional inverse/semi-inverse methods. Compared with the conventional methods, the employed method eliminates the need to preselect the deflection function, which makes it more reasonable and theoretical for calculating the mechanical responses of the plates. Moreover, the approach used can also analyze static problems of moderately thick plates and thick plates with the same boundary conditions investigated in this article. Finally, comprehensive analytical results obtained in this paper illuminate the validity of the proposed approach by comparing with the previous literature and finite element method by using (ABAQUS) software.

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“…Several numerical solutions are proposed to analyze the bending of plates with different edge conditions, loading pattern, and material properties by applying finite difference method (Karimi and Shahidi 2017), spline element method (Shen and He 1995), boundary element method (Paiva 2018), meshless method (Sator et al 2018), finite-element method (FEM) (Li and Kapania 2018), boundary particle method (Fu et al 2009), isogeometric collocation method (Pavan and Rao 2017), discrete singular convolution method (Civalek 2007;Civalek and Ersoy 2009;Civalek and Emsen 2009;Civalek and Acar 2007), differential quadrature method (Civalek 2004;Civalek and Ülker 2004), finite volume method (Wheel 1997), virtual element method (Brezzi and Marini 2013), finite-layer method (Timonin 2016), simple hp cloud method (Jafari and Azhari 2017), etc. However, the aforementioned numerical studies have some shortcoming, for instance, the convergence difficulties being time-consuming and tiring process compared to the analytical solution.…”

Section: Introductionmentioning

confidence: 99%

Analytical bending solutions of thin plates with two adjacent edges free and the others clamped or simply supported using finite integral transform method

et al. 2020

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The finite integral transform method is developed to explore the bending analysis of thin plates with the combination of simply supported, clamped, and free boundary conditions. Previous solutions mostly focused on simply supported and clamped boundary conditions, but the existence of free boundary conditions makes the solving process more complex, because it is difficult to find the exact solution which satisfies both deflection and internal force by conventional inverse/semi-inverse method or approximate method. Using this method, the plate high-order partial differential equation is simplified to a linear algebraic equation by the integral transformation. Then, through some mathematical manipulation, the analytical solution is elegantly achieved in a straightforward procedure. Compared with other methods, the present method is much simpler and general and does not need to pre-determine the deflection function, which makes it very attractive for calculating the mechanical responses of the plates. Comprehensive analytical results obtained in this paper illuminate the validity of the proposed method by comparison with the existing literature and finite-element method using (ABAQUS) software. Keywords Bending analysis • Analytical solution • Finite integral transform method • Rectangular thin plates Mathematics Subject Classification 45Axx Integral equations • 45Kxx Integro-partial differential equations • 45Qxx Inverse problems for integral equations Communicated by Apala Majumdar.

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Free vibration and bending analysis of circular Mindlin plates using singular convolution method

Cited by 17 publications

References 80 publications

Three-dimensional vibrations of annular thick plates with linearly varying thickness

Three-dimensional vibrations of annular thick plates with linearly varying thickness

Analytical Bending Solutions of Orthotropic Rectangular Thin Plates with Two Adjacent Edges Free and the Others Clamped or Simply Supported Using Finite Integral Transform Method

Analytical bending solutions of thin plates with two adjacent edges free and the others clamped or simply supported using finite integral transform method

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