Free vibration analysis of circular plates using generalized differential quadrature rule

Wu, T.Y.; Wang, Y.Y; Liu, G.R

doi:10.1016/s0045-7825(02)00463-2

Cited by 101 publications

(52 citation statements)

References 25 publications

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“…[1,6,9,10,16]. The numerical results for plates with sliding supports are shown in Table 5 with comparison to Refs.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The numerical results for plates with sliding supports are shown in Table 5 with comparison to Refs. [6,15]. The eigenvalues for plates with elastic supports and different values of elastic parameters on the edges are presented in Tables 6-8 with comparison to Refs.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The eigenvalues for plates with elastic supports and different values of elastic parameters on the edges are presented in Tables 6-8 with comparison to Refs. [6,15]. Table 2 The first ten lower dimensionless frequencies λ of free vibration of clamped circular plates Table 4 The first ten lower dimensionless frequencies λ of free vibration of simply supported circular plates Table 5 The first ten lower dimensionless frequencies λ of free vibration of circular plates with sliding edge Table 6 The first ten lower dimensionless frequencies λ of free vibration of circular plates with elastic supports (ϕ = 0.1; ψ = 100) Table 7 The first ten lower dimensionless frequencies λ of free vibration of circular plates with elastic supports (ϕ = 10; ψ = 100) Table 8 The first ten lower dimensionless frequencies λ of free vibration of circular plates with elastic supports (ϕ = 1000; ψ = 100)…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Chakraverty et al [3,4] have studied the free vibration analysis of plates of various geometries by using two-dimensional boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method. Wu and Liu [5,6] proposed the generalized differential quadrature rule (GDQR) to a free vibration analysis of circular thin plates. Jaroszewicz and Zoryj [7] have studied free vibration of circular thin plates of constant and linearly variable thickness using the method of partial discretization (MPD).…”

Section: Introductionmentioning

confidence: 99%

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Green’s function approach to frequency analysis of thin circular plates

Żur¹

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract.The free vibration analysis of homogeneous and isotropic circular thin plates by using the Green's functions is considered. The formulae for construction of the influence function for all nodal diameters are presented in a closed form. The limited independent solutions of differential Euler equations were expanded in the Neumann power series using the method of successive approximation. This approach allows to obtain the analytical frequency equations as power series rapidly convergent to exact eigenvalues for different number of nodal diameters.

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“…[1,6,9,10,16]. The numerical results for plates with sliding supports are shown in Table 5 with comparison to Refs.…”

Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Green’s function approach to frequency analysis of thin circular plates

Żur¹

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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“…For instance, in solving the free vibration problem of circular plates, Wu and Liu (2001) also Wu et al (2002) have also addressed this difficulty. They pointed out that some regularity conditions should be applied at the plate center in order to solve such type of problems.…”

Section: Regularity Conditions At R =mentioning

confidence: 99%

Pressure-Based and Potential-Based Differential Quadrature Procedures for Free Vibration of Circular Plates in Contact with Fluid

Eftekhari

2016

Lat. Am. j. solids struct.

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The differential quadrature method (DQM) has been so far applied to a wide variety of fluid and/or structural problems. The results of many researchers reveal that the DQM is computationally efficient and is applicable to a large class of boundary value problems. However, there is little information about its applications to fluidstructure interaction problems. Therefore, the purpose of this paper is to provide some information in this area and to develop procedures based on the DQM for the numerical solution of fluidstructure interaction problems. First, the governing partial differential equations of motion of the structure and fluid are discretized separately using the DQM. Then, by applying the boundary condition at fluid-structure interface, the governing eigenvalue equations of the coupled system are obtained which can then be solved for the eigenvalues of the system. The applicability of the proposed procedures is shown herein through the free vibration analysis of thin circular plates in contact with a cylindrical fluid-filled cavity. Issues related to the implementation of the regularity conditions at the center of the circular plate and the central line of the cylindrical cavity are addressed. Two new regularity conditions are proposed for the circular cylindrical fluid domain. The accuracy and efficiency of the proposed procedures are demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate converged results can be obtained by the proposed procedures using a small number of grid points. Three new dimensionless parameters and variables are also introduced for the free vibration of the coupled system. The influences of these parameters on dynamic behavior of the system are studied.

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

Cívalek

Ersoy

2008

Commun. Numer. Meth. Engng.

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SUMMARYCircular plates are important structural elements in modern engineering structures. In this paper a computationally efficient and accurate numerical model is presented for the study of free vibration and bending behavior of thick circular plates based on Mindlin plate theory. The approach developed is based on the discrete singular convolution method and the use of regularized Shannon's delta kernel. Frequency parameters, deflections and bending moments are obtained for different geometric parameters of the circular plate. Comparisons are made with existing numerical and analytical solutions in the literature. It is found that the DSC method yields accurate results for the free vibration and bending problems of thick circular plates.

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Free vibration analysis of circular plates using generalized differential quadrature rule

Cited by 101 publications

References 25 publications

Green’s function approach to frequency analysis of thin circular plates

Green’s function approach to frequency analysis of thin circular plates

Pressure-Based and Potential-Based Differential Quadrature Procedures for Free Vibration of Circular Plates in Contact with Fluid

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

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