Analysis of Vibrating Rectangular Plates With Non-Uniform Boundary Conditions By Using the Differential Quadrature Method

Laura, P.A.A.; Gutiérrez, R.H.

doi:10.1006/jsvi.1994.1255

Cited by 48 publications

(35 citation statements)

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“…Further, Case 13 (E}S}E}S) is considered for the numerical test of convergence. This problem has also been studied by other researchers [19,24,26]. Therefore, a comparison can be made with the existing literature and is given in the next subsection.…”

Section: Convergence Studymentioning

confidence: 97%

“…A variety of computational methods have been employed successfully for such analysis. These include the Rayleigh method [17], Ritz variational methods [18,19], methods of "nite strip [20,21] and spline "nite strip [22], the series expansion [23] for orthotropic plates, methods of di!erential quadrature [24] and generalized di!erential quadrature [25,26], etc. However, alternative approaches might provide better results for plate analysis.…”

Section: Introductionmentioning

confidence: 99%

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DSC Analysis of Rectangular Plates With Non-Uniform Boundary Conditions

Zhao¹,

Wei²

2002

Journal of Sound and Vibration

101

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This paper introduces the discrete singular convolution (DSC) for the vibration analysis of rectangular plates with non-uniform and combined boundary conditions. A systematic scheme is proposed for the treatment of boundary conditions required in the proposed approach. The validity of the DSC approach for plate vibration is tested by using a large number of numerical examples that have a combination of simply supported, clamped and transversely supported (with non-uniform elastic rotational restraint) edges. The present results are in excellent agreement with those in the literature.

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Section: Convergence Studymentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

DSC Analysis of Rectangular Plates With Non-Uniform Boundary Conditions

Zhao¹,

Wei²

2002

Journal of Sound and Vibration

101

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“…In order to overcome this di culty, three di erent methodologies were introduced by researchers. The ÿrst approach to be referred as the -technique was developed by Bert et al [8], and can be found in the works of Sherbourne and Pandey [10], Farsa et al [11], Laura and Gutierrez [12], Gutierrez and Laura [35], Striz et al [13], and Wang [14]. Jang et al [15] found that the method is not equally successful for all structural components with di erent boundary conditions if is not assumed very small.…”

Section: Introductionmentioning

confidence: 98%

Application of a new differential quadrature methodology for free vibration analysis of plates

Karami

Malekzadeh

2002

Numerical Meth Engineering

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SUMMARYA new methodology is introduced in the di erential quadrature (DQ) analysis of plate problems. The proposed approach is distinct from other DQ methods by employing the multiple boundary conditions in a di erent manner. For structural and plate problems, the methodology employs the displacement within the domain as the only degree of freedom, whereas along the boundaries the displacements as well as the second derivatives of the displacements with respect to the co-ordinate variable normal to the boundary in the computational domain are considered as the degrees of freedom for the problem. Employing such a procedure would facilitate the boundary conditions to be implemented exactly and conveniently. In order to demonstrate the capability of the new methodology, all cases of free vibration analysis of rectangular isotropic plates, in which the conventional DQ methods have had some sort of di culty to arrive at a converged or accurate solution, are carried out. Excellent convergence behaviour and accuracy in comparison with exact results and=or results obtained by other approximate methods were obtained. The analogous DQ formulation for a general rectangular plate is derived and for each individual boundary condition the general format for imposing the given conditions is devised. It must be emphasized that the computational e orts of this new methodology are not more than for the conventional di erential quadrature methods.

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“…Bert and his co-workers first used the DQ method to solve problems in structural mechanics in 1988 [2,3]. Since then, the method has been applied successfully to a variety of problems [4][5][6][7][8][9]. Details on the development of the DQ method and on its applications to structural mechanics problems may be found in References [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Static and free vibration analyses of rectangular plates by the new version of the differential quadrature element method

Wang

Zhou

2004

Numerical Meth Engineering

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SUMMARYA new version of the differential quadrature method is presented in this paper to overcome the difficulty existing in the ordinary differential quadrature method for applying multi-boundary conditions in twodimensional problems. Since the weighting coefficients of the first derivative are the same as for the ordinary differential quadrature method even with the introduction of multi-degree-of-freedom at the boundary points, the method is easier to extend to two-or three-dimensional problems. A new version of the differential quadrature plate element has been established for demonstration. The essential difference from the existing old version of the differential quadrature plate element is the way the weighting coefficients are determined. The methodology is worked out in detail and some numerical examples are given to show the efficiency of the present method.

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Analysis of Vibrating Rectangular Plates With Non-Uniform Boundary Conditions By Using the Differential Quadrature Method

Cited by 48 publications

References 0 publications

DSC Analysis of Rectangular Plates With Non-Uniform Boundary Conditions

DSC Analysis of Rectangular Plates With Non-Uniform Boundary Conditions

Application of a new differential quadrature methodology for free vibration analysis of plates

Static and free vibration analyses of rectangular plates by the new version of the differential quadrature element method

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