Free-Vibration Study of Thick Rectangular Plates using Polynomial Displacement Functions

Onyechere, I. C.; Ibearugbulem, O. M.; Anya, U. C.; Anyaogu, L.; Awodiji, Chioma Temitope Gloria

doi:10.36348/sjet.2020.v05i02.006

“…The use of polynomial deflection expression in the free vibration analysis of thick rectangular plates with two different edge conditions; one with its four edges clamped denoted with the acronym (CCCC) and another with two adjacent edges fixed and the other two adjacent edges having simple supports denoted with the acronym (CCSS) was investigated using a simple linear equation derived in [10] based on higher order shear deformation theory.…”

Section: Discussionmentioning

confidence: 99%

“…A plate is formed by grids of beams and these beams are arranged perpendicularly to each other. In combining them, the end conditions of the beam in x-direction (horizontal) are placed first before placing the end conditions of beam in y-direction (vertical) [2].…”

Section: Fig-1: Edge Conditions Of the Orthogonal Beamsmentioning

confidence: 99%

“…Thick plate theories differ from thin plate theories by the introduction of shear deformation effects on the displacements of the plate. The first published work on thick plate was carried out by Reisner in 1945 and was later refined by Mindlin in 1951 [1,2]. The Reisner-Mindlin theory is called the First Order Shear Deformation Theory (FSDT).…”

Section: Introductionmentioning

confidence: 99%

“…Used two-eigenfunctions to study free-vibration of thick plates. Polynomial deflection expression was used by [10] to study free-vibration of rectangular thick plates with simple supports at all the four edges [11] developed exact displacement expressions for analysis of thick plates. Buckling analysis of thick plates with simple supports at all the four edges using orthogonal polynomial displacement functions were investigated by [12,13].…”

Section: Introductionmentioning

confidence: 99%

“…Present study used a polynomial expression to represent the deflection to make the analysis quick and easy. A simple linear equation developed from a higher order shear deformation theory in the works of [10] was applied in free-vibration analysis of rectangular thick plates with all edges clamped and one with two adjacent edges clamped and the other two adjacent edges having simple supports.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Use of Polynomial Deflection Function in The Analysis of Thick Plates using Higher Order Shear Deformation Theory

Onyechere¹,

Ibearugbulem²,

Anya³

et al. 2020

SJCE

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In this work, polynomial deflection expression was used in the free-vibration investigation of thick rectangular plates with two different boundary conditions; one with its four edges clamped denoted with the acronym (CCCC) and another with two adjacent edges fixed and having simple supports at the other two adjacent edges denoted with the acronym (CCSS). The edge conditions of the various plates were fulfilled and used in generating the stiffness coefficients which were substituted into the analytical equation to obtain the non-dimensional frequency functions for the plates at different span-depth ratio (a/t) and aspect ratio (b/a). It was observed that at the same value of (b/a), there is an increase in the value of the non-dimensional frequency parameter as (a/t) increases. Also, at the same value of (a/t), there is a decrease in the value of the non-dimensional frequency parameter as (b/a) increases. The results obtained for the all edges clamped plate were compared with similar works by other researchers in the literature and were found to follow similar pattern and trend and were quite close.

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Flexural Analysis of Thick Isotropic Rectangular Plates Using Orthogonal Polynomial Displacement Functions

Dinwoke¹,

Henry²,

Franklin³

2021

EJ-ENG

0

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This paper analysed the flexural behaviour of SSSS thick isotropic rectangular plates under transverse load using the Ritz method. It is assumed that the line that is normal to the mid-surface of the plate before bending does not remain the same after bending and consequently a shear deformation function f (z) is introduced. A polynomial shear deformation function f (z) was derived for this research. The total potential energy which was established by combining the strain energy and external work was subjected to direct variation to determine the governing equations for the in – plane and out-plane displacement coefficients. Numerical results for the present study were obtained for the thick isotropic SSSS rectangular plates and comparison of the results of this research and previous work done in literature showed good convergence. However, It was also observed that the result obtained in this present study are significantly upper bound as compared with the results of other researchers who employed the higher order shear deformation theory (HSDT), first order shear deformation theory (FSDT) and classical plate theory (CPT) theories for the in – plane and out of plane displacements at span – depth ratio of 4. Also, at a span - depth ratio of and above, there was approximately no difference in the values obtained for the out of plane displacements and in-plane displacements between the CPT and the theory used in this study.

show abstract

Flexural Analysis of Thick Isotropic Rectangular Plates Using Orthogonal Polynomial Displacement Functions

Dinwoke

¹

,

Henry

²

,

Franklin

³

2021

EJENG

1

0

View full text Add to dashboard Cite

This paper analysed the flexural behaviour of SSSS thick isotropic rectangular plates under transverse load using the Ritz method. It is assumed that the line that is normal to the mid-surface of the plate before bending does not remain the same after bending and consequently a shear deformation function f (z) is introduced. A polynomial shear deformation function f (z) was derived for this research. The total potential energy which was established by combining the strain energy and external work was subjected to direct variation to determine the governing equations for the in – plane and out-plane displacement coefficients. Numerical results for the present study were obtained for the thick isotropic SSSS rectangular plates and comparison of the results of this research and previous work done in literature showed good convergence. However, It was also observed that the result obtained in this present study are significantly upper bound as compared with the results of other researchers who employed the higher order shear deformation theory (HSDT), first order shear deformation theory (FSDT) and classical plate theory (CPT) theories for the in – plane and out of plane displacements at span – depth ratio of 4. Also, at a span - depth ratio of and above, there was approximately no difference in the values obtained for the out of plane displacements and in-plane displacements between the CPT and the theory used in this study.

show abstract

Free-Vibration Study of Thick Rectangular Plates using Polynomial Displacement Functions

Cited by 6 publications

References 0 publications

The Use of Polynomial Deflection Function in The Analysis of Thick Plates using Higher Order Shear Deformation Theory

The Use of Polynomial Deflection Function in The Analysis of Thick Plates using Higher Order Shear Deformation Theory

Flexural Analysis of Thick Isotropic Rectangular Plates Using Orthogonal Polynomial Displacement Functions

Flexural Analysis of Thick Isotropic Rectangular Plates Using Orthogonal Polynomial Displacement Functions

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