• Geomechanics and Engineering
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• v.16 no.3
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• pp.257-271
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• 2018

In this paper, the effect of the homogenization models on buckling and free vibration is presented for simply supported functionally graded plates (FGM) resting on elastic foundation. The majority of investigations developed in the last decade, explored the Voigt homogenization model to predict the effective proprieties of functionally graded materials at the macroscopic-scale for FGM mechanical behavior. For this reason, various models have been used to derive the effective proprieties of FGMs and simulate thereby their effects on the buckling and free vibration of FGM plates based on comparative studies that may differ in terms of several parameters. The refined plate theory, as used in this paper, is based on dividing the transverse displacement into both bending and shear components. This leads to a reduction in the number of unknowns and governing equations. Furthermore the present formulation utilizes a sinusoidal variation of displacement field across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton's principle. Analytical solutions for the buckling and free vibration analysis are obtained for simply supported plates. The obtained results are compared with those predicted by other plate theories. This study shows the sensitivity of the obtained results to different homogenization models and that the results generated may vary considerably from one theory to another. Comprehensive visualization of results is provided. The analysis is relevant to aerospace, nuclear, civil and other structures.

• Steel and Composite Structures
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• v.20 no.2
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• pp.227-249
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• 2016

The objective of this work is to present a zeroth-order shear deformation theory for free vibration analysis of functionally graded (FG) nanoscale plates resting on elastic foundation. The model takes into consideration the influences of small scale and the parabolic variation of the transverse shear strains across the thickness of the nanoscale plate and thus, it avoids the employ use of shear correction factors. Also, in this present theory, the effect of transverse shear deformation is included in the axial displacements by using the shear forces instead of rotational displacements as in available high order plate theories. The material properties are supposed to be graded only in the thickness direction and the effective properties for the FG nanoscale plate are calculated by considering Mori-Tanaka homogenization scheme. The equations of motion are obtained using the nonlocal differential constitutive expressions of Eringen in conjunction with the zeroth-order shear deformation theory via Hamilton's principle. Numerical results for vibration of FG nanoscale plates resting on elastic foundations are presented and compared with the existing solutions. The influences of small scale, shear deformation, gradient index, Winkler modulus parameter and Pasternak shear modulus parameter on the vibration responses of the FG nanoscale plates are investigated.

• Journal of Biomedical Engineering Research
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• v.21 no.3 s.61
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• pp.285-293
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• 2000

Age-related changes in the geometry of human lumbar spine would lead to changes of its mechanical behaviors. To investigate the effects of the geometric changes, no age-related changes in the material/mechanical properties were considered. Using the finite element method. two age-related models of lumbar spine segments (L3-L4) were constructed. The annulus of the models was modeled as laminate composite elements with 16 layers and 6 materials. The spinal stiffness and facet reaction of the lumbar spine increased with the age-related geometric changes in various combined loadings. Fiber and transverse tensile strains of the inner annulus. cancellous bone stress and end-plate stress decreased with the age-related geometric changes whereas fiber/layer compressive strains of the annulus. facet reaction. ligament reaction and end-plate rigidity increased. Consequently, it appears that in the normal age-related deterioration of discs, the age-related geometric change contributes to the increase of spinal stiffness (the decrease in range of the motion segment), preventing an excessive deformation of the disc.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.38 no.12
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• pp.1051-1056
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• 2014

After hot rolling, a high-temperature steel plate with a temperature higher than $800^{\circ}C$ is rapidly cooled by multiple circular water jets. In this cooling process, because the temperature of the steel plate is much higher than the boiling point of the cooling water, film-boiling heat transfer occurs and a very thin steam layer forms between the plate surface and the cooling water. The steam layer acts as a thermal resistance that prevents heat transfer between the cooling water and the steel plate. In addition to the film-boiling heat transfer, complex physical phenomena such as the free-surface flow of residual water that accumulated on the material and the material's high-speed motion also occur in the cooling process. In this study, the simultaneous cooling process of the upper and lower sides of a running hot steel strip is investigated using a three-dimensional numerical model and the cooling performances and characteristics of the upper-side cooling and lower-side cooling are compared.

• Earthquakes and Structures
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• v.10 no.5
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• pp.1033-1048
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• 2016

An analytical solution based on the neutral surface concept is developed to study the free vibration behavior of simply supported functionally graded plate reposed on the elastic foundation by taking into account the effect of transverse shear deformations. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain obtained by using a new refined shear deformation theory. The foundation is described by the Winkler-Pasternak model. The Young's modulus of the plate is assumed to vary continuously through the thickness according to a power law formulation, and the Poisson ratio is held constant. The equation of motion for FG rectangular plates resting on elastic foundation is obtained through Hamilton's principle. Numerical examples are provided to show the effect of foundation stiffness parameters presented for thick to thin plates and for various values of the gradient index, aspect and side to thickness ratio. It was found that the proposed theory predicts the fundamental frequencies very well with the ones available in literature.

• Smart Structures and Systems
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• v.18 no.4
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• pp.787-800
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• 2016

The aim of the paper is to analyze nonlinear transverse vibration of an embedded piezoelectric plate reinforced with single walled carbon nanotubes (SWCNTs). The system in rested in a Pasternak foundation. The micro-electro-mechanical model is employed to calculate mechanical and electrical properties of nanocomposite. Using nonlinear strain-displacement relations and considering charge equation for coupling between electrical and mechanical fields, the motion equations are derived based on energy method and Hamilton's principle. These equations can't be solved analytically due to their nonlinear terms. Hence, differential quadrature method (DQM) is employed to solve the governing differential equations for the case when all four ends are clamped supported and free electrical boundary condition. The influences of the elastic medium, volume fraction and orientation angle of the SWCNTs reinforcement and aspect ratio are shown on frequency of structure. The results indicate that with increasing volume fraction of SWCNTs, the frequency increases. This study might be useful for the design and smart control of nano/micro devices such as MEMS and NEMS.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.19-31
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• 2018

In this paper, a new quasi-3D sinusoidal shear deformation theory for functionally graded (FG) plates is proposed. The theory considers both shear deformation and thickness-stretching influences by a trigonometric distribution of all displacements within the thickness, and respects the stress-free boundary conditions on the upper and lower faces of the plate without employing any shear correction coefficient. The advantage of the proposed model is that it posses a smaller number of variables and governing equations than the existing quasi-3D models, but its results compare well with those of 3D and quasi-3D theories. This benefit is due to the use of undetermined integral unknowns in the displacement field of the present theory. By employing the Hamilton principle, equations of motion are obtained in the present formulation. Closed-form solutions for bending and free vibration problems are determined for simply supported plates. Numerical examples are proposed to check the accuracy of the developed theory.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.15 no.3
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• pp.8-16
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• 2006

This paper discusses design sensitivity analysis and its application to a structural dynamics modification. Eigenvalue derivatives are determined with respect to the element parameters, which include intrinsic property parameters such as Young's modulus, density of the material, diameter of a beam element, thickness of a plate element, and shape parameters. Derivatives of stiffness and mass matrices are directly calculated by derivatives of element matrices. The first and the second order derivatives of the eigenvalues are then mathematically derived from a dynamic equation of motion of FEM model. The calculation of the second order eigenvalue derivative requires the sensitivity of its corresponding eigenvector, which are developed by Nelson's direct approach. The modified eigenvalue of the structure is then evaluated by the Taylor series expansion with the first and the second derivatives of eigenvalue. Numerical examples for simple beam and plate are presented. First, eigenvalues of the structural system are numerically calculated. Second, the sensitivities of eigenvalues are then evaluated with respect to the element intrinsic parameters. The most effective parameter is determined by comparing sensitivities. Finally, we predict the modified eigenvalue by Taylor series expansion with the derivatives of eigenvalue for single parameter or multi parameters. The examples illustrate the effectiveness of the eigenvalue sensitivity analysis for the optimization of the structures.

• Journal of Drive and Control
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• v.12 no.2
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• pp.7-13
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• 2015

In this study, we suggested the wave power generator using horizontal motions of the wave for use in the coastal sea. The length of the horizontal movement of the wave in the vicinity of the sea surface is larger than the length of the vertical reciprocating movement of the wave, hence the proposed device has a wave power transmission plate. In addition, because the motion of the wave is maximum to the sea surface, by arranging the buoyancy tanks at the top of the wave power transmission plate, it is always capable of vertical movement in accordance with the sea surface. To confirm the usefulness of the proposed wave power generator, we constructed a mathematical model of the wave power generator and carried out simulation using bondgraph. Furthermore, the efficiency was verified by measuring the degree of electrical energy production through a preliminary experiment.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.3
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• pp.14-21
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• 2006

The unsteady vortex lattice method is used to model twisting and flapping motions of a rectangular flat plate wing. The results for plunging and pitching motions were compared with the limited experimental results available and other numerical methods. They show that the method is capable of simulating many of the features of complex flapping flight. The lift, thrust and propulsive efficiency of a rectangular flat plate wing have been calculated for various twisting angles and reduced frequency with an amplitude of flapping angle($20^{\circ}$). And the effects of the twisting on the aerodynamic characteristics of the flapping wing are discussed by examination of their trends.