• Tribology and Lubricants
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• v.21 no.6
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• pp.283-288
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• 2005

This paper presents the theoretical model and analysis results to investigate the effect of Coulomb damping in the sub-structure of a foil bearing. Vertical and horizontal deflection of a bump is restricted by friction of the bump. Equivalent viscous damping of the bump foil is derived from the Coulomb friction. Dynamic equation of the bump is constituted by stiffness and damping terms. The air film is modeled by the compressible Reynolds equation. A perturbation approach and finite difference numerical method is used to determine the static and dynamic performance of the bearing from the coupled fluid-structural model. The analysis result shows that the static and dynamic performance is enhanced by the bump friction.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.9 s.90
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• pp.846-851
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• 2004

Static and dynamic responses of micro cantilever beam structures undertaking electrostatic forces are obtained employing Galerkin's method based on Euler beam theory. Variations of static and dynamic responses as well as resonant frequencies are estimated for several sets of beam properties and applied voltages. It is shown that the applied voltage influences the deflection and the modal characteristics significantly. Such information can be usefully employed for the design of MEMS structures.

• Steel and Composite Structures
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• v.49 no.4
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• pp.431-440
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• 2023

The functionally graded (FG) porous plates are usually characterized by the non-symmetric elastic modulus distribution through the thickness so that the plate neutral surface does not coincide with the mid-surface. Nevertheless, the conventional analysis models were mostly based on the plate mid-surface so that the accuracy of resulting numerical results is questionable. In this context, this paper presents the neutral surface-based static and free vibration analysis of FG porous plates and investigates the differences between the mid- and neutral surface-based analysis models. The neutral surface-based numerical method is formulated using the (3,3,2) hierarchical model and approximated by the last introduced natural element method (NEM). The volume fractions of metal and ceramic are expressed by the power-law function and the cosine-type porosity distributions are considered. The proposed numerical method is demonstrated through the benchmark experiment, and the differences between two analysis models are parametrically investigated with respect to the thickness-wise material and porosity distributions. It is found from the numerical results that the difference cannot be negligible when the material and porosity distributions are remarkably biased in the thickness direction.

• Structural Engineering and Mechanics
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• v.65 no.5
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• pp.573-585
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• 2018

This article presents strain gradient elasticity-based procedures for static bending, free vibration and buckling analyses of functionally graded rectangular micro-plates. The developed method allows consideration of smooth spatial variations of length scale parameters of strain gradient elasticity. Governing partial differential equations and boundary conditions are derived by following the variational approach and applying Hamilton's principle. Displacement field is expressed in a unified way to produce numerical results in accordance with Kirchhoff, Mindlin, and third order shear deformation theories. All material properties, including the length scale parameters, are assumed to be functions of the plate thickness coordinate in the derivations. Developed equations are solved numerically by means of differential quadrature method. Proposed procedures are verified through comparisons made to the results available in the literature for certain limiting cases. Further numerical results are provided to illustrate the effects of material and geometric parameters on bending, free vibrations, and buckling. The results generated by Kirchhoff and third order shear deformation theories are in very good agreement, whereas Mindlin plate theory slightly overestimates static deflection and underestimates natural frequency. A rise in the length scale parameter ratio, which identifies the degree of spatial variations, leads to a drop in dimensionless maximum deflection, and increases in dimensionless vibration frequency and buckling load. Size effect is shown to play a more significant role as the plate thickness becomes smaller compared to the length scale parameter. Numerical results indicate that consideration of length scale parameter variation is required for accurate modelling of graded rectangular micro-plates.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2005.04a
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• pp.240-244
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• 2005

In this study a simple model is developed that predicts impact damage in a composite laminate using an analytical model. The model uses a non-linear approximation method (Rayleigh-Ritz) and the large deflection plate theory to predict the number of failed plies and damage area in a quasi-isotropic composite circular plate (axisymmetric problem) due to a point impact load at its centre. It is assumed that the deformation due to a static transverse load is similar to that occurred in a low velocity impact. It is found that the model, despite its simplicity, is in good agreement with FEM predictions and experimental data for the deflection of the composite plate and gives a good estimate of the number of failed plies due to fibre breakage. The predicted damage zone could be used with a fracture mechanics model developed by the second investigator and co-workers to calculate the compression after impact strength of such laminates. This approach could save significant running time when compared to FEM solutions.

• Advances in Computational Design
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• v.2 no.3
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• pp.165-194
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• 2017

The present work proposes the thermo mechanically induced statistics of nonlinear transverse central deflection of elastically supported functionally graded (FG) plate subjected to static loadings with random system properties. The FG plate is supported on two parameters Pasternak foundation with Winkler cubic nonlinearity. The random system properties such as material properties of FG material, external loading and foundation parameters are assumed as uncorrelated random variables. The material properties are assumed as non-uniform temperature distribution with temperature dependent (TD) material properties. The basic formulation for static is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strain kinematics through Newton-Raphson method. A second order perturbation technique (SOPT) and direct Monte Carlo simulation (MCS) are used to compute the nonlinear governing equation. The effects of load parameters, plate thickness ratios, aspect ratios, volume fraction, exponent, foundation parameters, and boundary conditions with random system properties are examined through parametric studies. The results of present approaches are compared with those results available in the literature and by employing direct Monte Carlo simulation (MCS).

• Journal of the Korea institute for structural maintenance and inspection
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• v.7 no.1
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• pp.157-163
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• 2003

Recently, the number of Prestressed Concrete(PSC) bridges needed repair and retrofit because of the increase of heavy traffic loads and aging of concrete materials. But there are a few related researches about strengthening PSC bridges. In this study, the practicability of strengthening methods for PSC beam were studied by the static experimental method. PSC beams in length of 6m were made with concrete slabs. Glass fiber sheeting and external post-tensioning methods were used for strengthening PSC beams. Some beams were strengthened after cracks to investigate the applicability for cracked bridges. As a result, there strengthening methods were efficient at increasing the cracking loads and the failure load, to decrease deflection and prevent cracks. In the case of using glass fiber retrofit methods, it should be careful in the anchorage problems for preventing the bonding failure.

• Structural Engineering and Mechanics
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• v.59 no.3
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• pp.431-454
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• 2016

In this paper, the nonlinear static and free vibration analysis of Euler-Bernoulli composite beam model reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) with initial geometrical imperfection under uniformly distributed load using finite element method (FEM) is investigated. The governing equations of equilibrium are derived by the Hamilton's principle and von Karman type nonlinear strain-displacement relationships are employed. Also the influences of various loadings, amplitude of the waviness, UD, USFG, and SFG distributions of carbon nanotube (CNT) and different boundary conditions on the dimensionless transverse displacements and nonlinear frequency ratio are presented. It is seen that with increasing load, the displacement of USFG beam under force loads is more than for the other states. Moreover it can be seen that the nonlinear to linear natural frequency ratio decreases with increasing aspect ratio (h/L) for UD, USFG and SFG beam. Also, it is shown that at the specified value of (h/L), the natural frequency ratio increases with the increasing the values amplitude of waviness while the dimensionless nonlinear to linear maximum deflection decreases. Moreover, with considering the amplitude of waviness, the stiffness of Euler-Bernoulli beam model reinforced by FG-CNT increases. It is concluded that the R parameter increases with increasing of volume fraction while the rate of this parameter decreases. Thus one can be obtained the optimum value of FG-CNT volume fraction to prevent from resonance phenomenon.

• Structural Engineering and Mechanics
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• v.59 no.3
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• pp.579-599
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• 2016

In this study, static bending of edge cracked micro beams is studied analytically under uniformly distributed transverse loading based on modified couple stress theory. The cracked beam is modelled using a proper modification of the classical cracked-beam theory consisting of two sub-beams connected through a massless elastic rotational spring. The deflection curve expressions of the edge cracked microbeam segments separated by the rotational spring are determined by the Integration method. The elastic curve functions of the edge cracked micro beams are obtained in explicit form for cantilever and simply supported beams. In order to establish the accuracy of the present formulation and results, the deflections are obtained, and compared with the published results available in the literature. Good agreement is observed. In the numerical study, the elastic deflections of the edge cracked micro beams are calculated and discussed for different crack positions, different lengths of the beam, different length scale parameter, different crack depths, and some typical boundary conditions. Also, the difference between the classical beam theory and modified couple stress theory is investigated for static bending of edge cracked microbeams. It is believed that the tabulated results will be a reference with which other researchers can compare their results.

• Steel and Composite Structures
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• v.51 no.6
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• pp.601-617
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• 2024

This work aims to explore the static behaviour of a tapered functionally graded porous plate (FGPP) with even and uneven porosity distributions resting on two parametric elastic foundations. The plate under investigation is subjected to bi-sinusoidal loading and the edges of the plate are exposed to different combinations of edge restrictions. In order to examin the static behaviour, bending factors (BF) related to bending and normal stresses have been evaluated using classical plate theory. To achieve this, the governing equations have been derived employing the energy concept. And to solve it, the Rayleigh-Ritz method with an algebraic function has been utilised; it is simple, precise, and computationally intensive. After convergence and validation analyses, new findings are made available. The BF of the plate have been exhaustively examined to explain the influence of aspect ratios, material property index, porosity factor, taper factor, and Winkler and Pasternak stiffness. It is observed that the BF of an elastically supported FGPP are influenced by the index of material propery and the aspect ratio. Findings also indicate that the impact of porosity is more when it is spread evenly, as opposed to when it is unevenly distributed. Further, the deformed plate's structure is significantly influenced by the different thickness variations. Examination of bending characteristics of FGPP having different new cases of thickness variations with different types of porosity distribution under fifteen different mixed edge constraints is the prime novality of this work. Results presented are reliable enough to be taken into account for future studies.