Vibration of skew plates resting on point supports

Mizusawa, T.; Kajita, Tateo

doi:10.1016/0022-460x(87)90470-6

Cited by 37 publications

(12 citation statements)

References 34 publications

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“…The ÿrst ÿve natural frequencies for a square plate with all four corners on rigid supports are presented in Table XI. An excellent agreement with the results by Misuzawa and Kajita [31] and also those of Bardell [30] was achieved. The negligible di erences between the results of Misuzawa, Kajita and Bardell with those of Hinton and Al-Janbi [33] are due to the fact that the e ects of shear deformation were neglected.…”

Section: S-s-s-s S-c-s-c S-c-s-s S-c-s-f S-s-s-f and S-f-s-f) Aresupporting

confidence: 85%

“…This problem that represents a highly complex-type boundary condition can be easily and systematically solved by DQM and especially by the present methodology. As far as the results are concerned good agreements have been achieved with the results by Misuzawa and Kajita [31] and in special with those of HFEM by Bardell [30] (see Table XII). The stability and convergence of the solution are evident.…”

Section: Plates With Mixed Supportssupporting

confidence: 70%

“…An interesting mixed boundary type problem, that is a square plate with two adjacent edges clamped, and the opposing corner points supported, to be named C-C-F-Fp (see Figure 3) was considered by Misuzawa and Kajita [31] and Bardell [30]. This problem that represents a highly complex-type boundary condition can be easily and systematically solved by DQM and especially by the present methodology.…”

Section: Plates With Mixed Supportsmentioning

confidence: 95%

“…Misuzawa and Kajita [31] have used Rayleigh-Ritz method with B-spline functions to study such problems. Hinton and Al-Janbi [33] have used a nine-node Mindlin plate-bending element and Bardell [30] has used the HFEM for such analysis.…”

Section: S-s-s-s S-c-s-c S-c-s-s S-c-s-f S-s-s-f and S-f-s-f) Arementioning

confidence: 99%

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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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Section: S-s-s-s S-c-s-c S-c-s-s S-c-s-f S-s-s-f and S-f-s-f) Aresupporting

confidence: 85%

Section: Plates With Mixed Supportssupporting

confidence: 70%

Section: Plates With Mixed Supportsmentioning

confidence: 95%

Section: S-s-s-s S-c-s-c S-c-s-s S-c-s-f S-s-s-f and S-f-s-f) Arementioning

confidence: 99%

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

Karami

Malekzadeh

2002

Numerical Meth Engineering

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“…These include vibrating beam functions (Kerstens, 1979), B-spline functions (Mizusawa and Kajita, 1987)] and orthogonal polynomial functions (Kim and Dickinson, 1987). On the other hand, Liew and Lam (1994) applied a set of orthogonal plate functions generated by using the Gram-Schmidt orthogonality relationship to elastic point supported rectangular plates.…”

Section: Introductionmentioning

confidence: 99%

The free vibration analysis of point supported rectangular plates using quadrature element method

Çetkin

Orak

2017

jtam

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In this study, the hybrid approach of the Quadrature Element Method (QEM) has been employed to generate solutions for point supported isotropic plates. The Hybrid QEM technique consists of a collocation method with the Galerkin finite element technique to combine the high accurate and rapid converging of Differential Quadrature Method (DQM) for efficient solution of differential equations. To present the validity of the solutions, the results have been compared with other known solutions for point supported rectangular plates. In addition, different solutions are carried out for different type boundary conditions, different locations and number of point supports. Results for the first vibration modes of plates are also tested using a commercial finite element code, and it is shown that they are in good agreement with literature.

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Vibration of shear‐deformable rectangular plates using a spline‐function Rayleigh‐Ritz approach

Wang¹,

Dawe²

1993

Numerical Meth Engineering

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SUMMARYThe prediction of the natural frequencies of vibration of rectangular plates or. orthotropic laminates is described, through the use of B-spline functions as trial functions in a Rayleigh-Ritz approach. Throughthickness shear deformation effects are included in the analysis and hence assumptions have to be made for the spatial variation over the plate middle surface of each of the lateral deflection and the two rotation components. Two versions of the splinc-function Rayleigh-Ritz approach are described: in one of these the deflection and rotations are represcnted by functions of the same polynomial order, whilst in the other a lower-order representation is used for cach rotation component in one of the co-ordinate directions. It is shown in a number of applications that the former version leads to shear-locking behaviour whilst the latter version avoids this behaviour and is suitable for the analysis of both thick and thin plates.

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Vibration of skew plates resting on point supports

Cited by 37 publications

References 34 publications

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

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

The free vibration analysis of point supported rectangular plates using quadrature element method

Vibration of shear‐deformable rectangular plates using a spline‐function Rayleigh‐Ritz approach

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