• Structural Engineering and Mechanics
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• v.87 no.3
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• pp.283-296
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• 2023

Free-vibration and buckling analyses of plate problems are investigated with the aid of the strain gradient notation finite element method (SGN-FEM). As SGN-FEM employs physically interpretable polynomials in developing finite elements, parasitic shear sources, which are the cause of shear locking, can be precisely identified and subsequently eliminated. This allows two mutually complementary objectives to be defined in this work, namely, evaluate the efficiency of free-vibration and buckling results provided by corrected models, and study the severity of parasitic shear effects on plate models performance. Parasitic shear are flexural terms erroneously present in shear strain polynomials. It is reviewed here that six parasitic shear terms arise during the formulation of the four-node Mindlin plate element. Two parasitic shear terms have been identified in the in-plane shear strain polynomial while other two have been identified in each of the transverse shear strain polynomials. The element is corrected a-priori, i.e., during development, by simply removing the spurious terms from the shear strain polynomials. The computational implementation of the element in its two versions, namely, containing the parasitic shear terms (PS) and corrected for parasitic shear (SG), allows for assessments of the accuracy of results and of the deleterious effects of parasitic shear in free vibration and buckling analyses. This assessment of the parasitic shear effects is a novelty of this work. Validation of the SG model is done comparing its results with analytical results and results provided by other numerical procedures. Analyses are performed for square plates with different thickness-to-length ratios and boundary conditions. Results for thin plates provided by the PS model do not converge to the correct solutions, which indicates that parasitic shear must be eliminated. That is, analysts should not rely on refinement alone. For thick plates, PS model results can be considered acceptable as deleterious effects are really critical in thin plates. On the other hand, results provided by the SG model converge well for both thin and thick plates. The effectiveness of the SG model is established via high-accuracy results obtained in several examples. It is concluded that corrected SGN-FEM models are efficient alternatives for free-vibration and buckling analysis of Mindlin plate problems, and that precise elimination of parasitic shear is a requirement for sound analyses.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.6
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• pp.529-538
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• 2016

The simplified plate theory is presented for static and free vibration analysis of power-law(P) and sigmoid(S) Functionally Graded Materials(FGM) plates. This theory considers the parabolic distribution of the transverse shear stress, and satisfies the condition that requires the transverse shear stress to be zero on the upper and lower surfaces of the plate, without the shear correction factor. The simplified plate theory uses only four unknown variables and shares strong similarities with classical plate theory(CPT) in many aspects such as stress-resultant expressions, equation of motion and boundary conditions. The material properties of the plate are assumed to vary according to the power-law and sigmoid distributions of the volume fractions of the constituents. The Hamilton's principle is used to derive the equations of motion and Winkler-Pasternak elastic foundation model is employed. The results of static and dynamic responses for a simply supported FGM plate are calculated and a comparative analysis is carried out. The results of the comparative analysis with the solutions of references show relevant and accurate results for static and free vibration problems of FGM plates. Analytical solutions for the static and free vibration problems are presented so as to reveal the effects of the power law index, elastic foundation parameter, and side-to-thickness ratio.

• Structural Engineering and Mechanics
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• v.75 no.2
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• pp.193-209
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• 2020

This paper presents a new hyperbolic shear deformation plate theory including the stretching effect for free vibration of the simply supported functionally graded plates in thermal environments. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. This theory has only five unknowns, which is even less than the other shear and normal deformation theories. The present one has a new displacement field which introduces undetermined integral variables. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume power laws of the constituents. The equation of motion of the vibrated plate obtained via the classical Hamilton's principle and solved using Navier's steps. The accuracy of the proposed solution is checked by comparing the present results with those available in existing literature. The effects of the temperature field, volume fraction index of functionally graded material, side-to-thickness ratio on free vibration responses of the functionally graded plates are investigated. It can be concluded that the present theory is not only accurate but also simple in predicting the natural frequencies of functionally graded plates with stretching effect in thermal environments.

• Steel and Composite Structures
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• v.41 no.6
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• pp.899-910
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• 2021

A 4-unknown shear deformation theory is applied to investigate the vibration of functionally graded plates under thermal environment. The plate is fabricated from a functionally graded material mixed of ceramic and metal with continuously varying material properties through the plate thickness. Three types of thermal loadings, uniform, linear and nonlinear temperature rises along the plate thickness are taken into account. The present theory contains four unknown functions as against five or more in other higher order shear deformation theories. The through-the-thickness distributions of transverse shear stresses of the plate are considered to vary parabolically and vanish at upper and lower surfaces. The present model does not require any problem dependent shear correction factor. Analytical solutions for the free vibration analysis are derived based on Fourier series that satisfy the boundary conditions (Navier's method). Benchmark solutions are firstly considered to evaluate the accuracy of the proposed model. Comparisons with the solutions available in literature revealed the good capabilities of the present model for the simulations of vibration responses of FG plates. Some parametric studies are carried out for the frequency analysis by varying the volume fraction profile and the temperature distribution across the plate thickness.

• Proceedings of the KSR Conference
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• 2010.06a
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• pp.13-17
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• 2010

This presentation examines the characteristics of torsional vibration in axisymmetric out-of-plane vibrations of an annular Mindin plate. The out-of-plane vibration of circular or annular plates have been investigated since a long years ago by many researchers. When the classical Kirchhoff plate theory neglecting the effect of transverse shear deformation is applied to a thick plate, its out-of-plane natural frequencies are much different from reality. And so, since Minlin presented a plate theory considering the effect of rotary inertia and transverse shear deformation, many researches for the out-of-plane natural vibration of circular or annular Mindin plates have been performed. But almost all researchers missed the torsional vibration due to transverse shear deformation in axisymmetric out-of-plane vibrations of the circular or annular Mindin plate. Therefore, in this presentation, we verify the existence of torsional vibration of an annular plate and present the natural frequencies of an annular plate with free outer boundary surface.

• Nuclear Engineering and Technology
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• v.47 no.4
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• pp.500-511
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• 2015

In this study, the natural frequencies of the perforated square plate with a square penetration pattern are obtained as a function of ligament efficiency using the commercial finite-element analysis code ANSYS. In addition, they are used to extract the effective modulus of elasticity under an assumption of a constant Poisson's ratio. The effective modulus of elasticity of the fully perforated square plate is applied to the modal analysis of a partially perforated square plate using a homogeneous finite-element analysis model. The natural frequencies and the corresponding mode shapes of the homogeneous model are compared with the results of the detailed finite-element analysis model of the partially perforated square plate to check the validity of the effective modulus of elasticity. In addition, the theoretical method to calculate the natural frequencies of a partially perforated square plate with fixed edges is suggested according to the Rayleigh-Ritz method.

• Wind and Structures
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• v.28 no.6
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• pp.347-354
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• 2019

This study provides an approximate analytical solution to the fractional vibration problem of thin plate governing anomalous motion of plate subjected to in-plane loads. The method of variable separable is employed to transform the fractional partial differential equations under consideration into a fractional ordinary differential equation in temporal variable and a bi-harmonic plate equation in spatial variable. The technique of conformable fractional derivative is utilized to solve the resulting fractional differential equation and the approach of finite sine integral transform method is used to solve the accompanying bi-harmonic plate equation. The deflection field which measures the transverse displacement of the plate is expressed in terms of product of Bessel and trigonometric functions via the temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem of thin plate in literature. This work shows that conformable fractional derivative is an efficient mathematical tool for tracking analytical solution of fractional partial differential equation governing anomalous vibration of thin plates.

• Composites Research
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• v.30 no.5
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• pp.273-279
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• 2017

This paper describes the fabrication techniques and analysis of hybrid composite plates with an active frequency selective surface (FSS). For fabricating hybrid composite plate with active FSS, an active FSS with a resonance frequency located in the C band can obtained using varactor diodes. The hybrid composite plate was first designed and simulated to determine its electromagnetic properties using the commercial software HFSS. After simulation, active FSSs and hybrid composite plates were fabricated by mounting with varactor diodes. After fabrication, free space measurement was used to determine the electromagnetic properties of active FSS and the hybrid composite plates. The simulation and experimental results were in good agreement.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.295-300
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• 2005

An analytical method for the hydroelastic vibration of a vessel composed of an upper annular plate and a lower circular plate is developed by the Rayleigh-Ritz method. The two plates are clamped along a rigid cylindrical vessel wall. It is assumed that the fluid bounded by a rigid cylindrical vessel is incompressible and non-viscous. The wet mode shape of the plates is assumed as a combination of the dry mode shapes of the plates. The fluid motion is described by using the fluid displacement potential and determined by using the compatibility conditions along the fluid interface with the plate. Minimizing the Rayleigh quotient based on the energy conservation gives an eigenvalue problem. It is found that the theoretical results can predict well the fluid-coupled natural frequencies comparing with the finite element analysis result.

• Journal of KSNVE
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• v.4 no.3
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• pp.283-295
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• 1994

This work presents the experimental and finite element analysis results for the free vibration of 4 edges clamped, isotropic square plates with 2 collinear circular holes. Natural frequencies of finite element analysis are obtained for the complete square plate, the square plates with a central circular hole and the square plates with 2 collinear circulare holes. And natural frequencies are experimentally measured for the complete square plate, the square plate with a central circular hole(d = 150 mm) and the square plates with 2 collinear circular holes. Agreement between experimental and FEM results is excellent. Mode shapes in special case are presented. The conclusions of the study are as follows. There is little variation of nondimensional frequency parameters for the first six mode when the aspect ratio of circular hole is less than 1/6 in the isotropic square plates with 2 collinear circular holes. And the first nondimensional frequency parameter doesn't vary as the aspect ratio of circular hole increase.