Free Vibration of Tapered Mindlin Plates Using Basic Displacement Functions

Pachenari, Zahra; Attarnejad, Reza

doi:10.1007/s13369-014-1071-1

Cited by 10 publications

(3 citation statements)

References 38 publications

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“…For general boundary conditions, however, the analytical solution cannot be obtained due to the complexities introduced by the satisfaction of free edges and free corner boundary conditions. So, various approximate or numerical methods such as the Ritz method [1,7,8], the differential quadrature method (DQM) [9][10][11][12], the method of superposition [13], the extended Kantorovich approach [14,15], the spectral finite element method [16], the finite element method with basic displacement functions [17], the finite element method with isogeometric analysis [18], the mesh-free method [19], BEM-based meshless method [20], the moving least squares differential quadrature method [21], semi-analytic differential quadrature method [22], the projection equation approach [23], the finite difference method [24], the spectral element method [25], the discrete singular convolution method [26][27][28], the radial basis function-based DQM [29,30], the weak-form DQM [31], and the strong-form finite element method [32][33][34] have been developed to study the behavior of rectangular plates with general boundary conditions. Among the approximate analytical methods utilized for addressing the present problem, the Ritz method is one the most convenient methods to obtain the natural frequencies of rectangular plates [1,[35][36][37].…”

Section: Introductionmentioning

confidence: 99%

A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free corners

Eftekhari

2016

Ain Shams Engineering Journal

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It is well known that the classical global approximation methods such as the conventional Ritz method and the conventional differential quadrature method (DQM) have some difficulty in determining the natural frequencies of rectangular plates involving free corners. The mixed Ritz-DQM formulation, which has been recently developed by the present author, was also shown to have such difficulty. This is because it is very difficult to implement the free corner boundary condition in these methods. To overcome this difficulty, this paper presents a mixed Ritz-DQM formulation in which the free corner boundary condition is implemented in a simple and easy manner. First, we present a new scheme for implementing multiple boundary conditions in the DQM discretized equations. By the help of this scheme, we then show that the free corner boundary condition can also be easily implemented in the final matrix equations of the Ritz-DQM approach. Finally, we validate the effectiveness of the proposed approach through numerical experiments. Numerical results show the advantages of the proposed method over some versions of the DQM in terms of accuracy and performance. Ó 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Section: Introductionmentioning

confidence: 99%

A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free corners

Eftekhari

2016

Ain Shams Engineering Journal

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“…Furthermore, Cheung and Zhou [17] have employed the Rayleigh method for computation, of free vibration solution, of rectangular plate having variable thickness. Pachenari and Attarnejad [18] presented the novel form to calculate new shape functions of the isotropic plate with tapered thickness for vibration analysis. Kumar et al [19] presented the model, of variable thick plate made of FGM in one direction, for free vibration analysis with different boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Vibration response of shear deformable functionally graded material plate with parabolic variable thickness

Kumar¹,

Singh²,

Saran

et al. 2022

IOP Conf. Ser.: Mater. Sci. Eng.

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This work presents the semi-analytical solution of vibration response for functionally graded materials (FGM) plates with bi-linear and parabolic variable thickness. Continuous thickness variation may affect the design of plate structure which permits to modify the stiffness properties in the utmost stressed area within the domain, considering the overall weight parameter of the structure. As a result, a better dynamic response may be revealed. The first order shear deformation theory (FSDT) has been applied for a kinematic model of the variable thick plate. The material properties were calculated by the simple power law. Accuracy of this model is confirmed by various comparisons with outcomes available in the preceding literature. Frequency factor of the plates with boundary conditions are found by changing the various parameter like material volume exponent, aspect ratio, tapered ratio and thickness ratio.

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“…This limitation is caused by the complexities introduced by the satisfaction of the free edges and free corner boundary conditions. To overcome the limitations of the analytical methods, various approximate or numerical methods such as the Ritz method [3][4][5][6], the extended Kantorovich approach [7], the nite element method [8,9], the BEM-based meshless method [10], the moving least squares di erential quadrature method [11], semianalytic di erential quadrature method [12], thenite di erence method [13], the spectral element method [14], and the discrete singular convolution method [15,16] have been developed by researchers to study the behavior of rectangular or other shaped plates with general boundary conditions. Among the approximate methods used for solving the present problem, the Di erential Quadrature Method (DQM) is one of the most convenient methods to obtain natural frequencies of rectangular plates [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

A dierential quadrature procedure for free vibration of rectangular plates involving free corners

Eftekhari

Jafari

2016

Scientia Iranica

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Abstract. The Di erential Quadrature Method (DQM) is one of the most powerful approximation methods for analyzing the free vibration of rectangular plates. It is easy to use and straightforward to implement. However, in spite of its many advantages, the conventional DQM has some limitations in determining the natural frequencies of rectangular plates involving free corners. This is because it is very di cult to implement the free corner boundary condition in conventional DQM. As a result, the method may exhibit some convergence problems and this may lead to erroneous and oscillatory results for natural frequencies of rectangular plates involving free corners. To overcome this di culty, this paper presents a simple DQM formulation in which all the natural boundary conditions, including the free corner boundary condition, are implemented in an easy manner. Its accuracy and e ciency are demonstrated through the vibration analysis of rectangular plates with di erent combinations of free edges and free corners. Numerical results prove that the proposed method can produce much better accuracy than the conventional DQM while exhibiting a monotonic convergence behavior with respect to the number of sampling points. Furthermore, unlike the conventional DQM, solutions of the proposed method are not very sensitive to the sampling point distribution.

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Free Vibration of Tapered Mindlin Plates Using Basic Displacement Functions

Cited by 10 publications

References 38 publications

A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free corners

A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free corners

Vibration response of shear deformable functionally graded material plate with parabolic variable thickness

A dierential quadrature procedure for free vibration of rectangular plates involving free corners

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