• Steel and Composite Structures
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• v.24 no.2
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• pp.151-176
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• 2017

This paper deals with general equations of motion for free vibration analysis response of thick three-layer doubly curved sandwich panels (DCSP) under simply supported boundary conditions (BCs) using higher order shear deformation theory. In this model, the face sheets are orthotropic laminated composite that follow the first order shear deformation theory (FSDT) based on Rissners-Mindlin (RM) kinematics field. The core is made of orthotropic material and its in-plane transverse displacements are modeled using the third order of the Taylor's series extension. It provides the potentiality for considering both compressible and incompressible cores. To find these equations and boundary conditions, Hamilton's principle is used. Also, the effect of trapezoidal shape factor for cross-section of curved panel element ($1{\pm}z/R$) is considered. The natural frequency parameters of DCSP are obtained using Galerkin Method. Convergence studies are performed with the appropriate formulas in general form for three-layer sandwich plate, cylindrical and spherical shells (both deep and shallow). The influences of core stiffness, ratio of core to face sheets thickness and radii of curvatures are investigated. Finally, for the first time, an optimum range for the core to face sheet stiffness ratio by considering the existence of in-plane stress which significantly affects the natural frequencies of DCSP are presented.

• Smart Structures and Systems
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• v.20 no.4
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• pp.509-524
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• 2017

In this article, a free vibration analysis of functionally graded (FG) plates resting on elastic foundations is presented using a quasi-3D hybrid-type higher order shear deformation theory. Undetermined integral terms are employed in the proposed displacement field and modeled based on a hybrid-type (sinusoidal and parabolic) quasi-3D HSDT with five unknowns in which the stretching effect is taken into account. Thus, it can be said that the significant feature of this theory is that it deals with only 5 unknowns as the first order shear deformation theory (FSDT). The elastic foundation parameters are introduced in the present formulation by following the Pasternak (two-parameter) mathematical model. Equations of motion are obtained via the Hamilton's principles and solved using Navier's method. Accuracy of the proposed theory is confirmed by comparing the results of numerical examples with the ones available in literature.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.1160-1165
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• 2004

The purpose of this study was to calculate three dimensional angular displacements, moments and joint reaction forces of the ankle joint during the waist pulling, and to assess the ankle joint reaction forces according to different perturbation modes and different levels of perturbation magnitude. Ankle joint model was assumed 3-D ball and socket joint which is capable of three rotational movements. We used 6 cameras, force plate and waist pulling system. Two different waist pulling systems were adopted for forward sway with three magnitudes each. From motion data and ground reaction forces, we could calculate 3-D angular displacements, moments and joint reaction forces during the recovery of postural balance control. From the experiment using falling mass perturbation, joint moments were larger than those from the experiment using air cylinder pulling system with milder perturbation. However, JRF were similar nevertheless the difference in joint moment. From this finding, we could conjecture that the human body employs different strategies to protect joints by decreasing joint reaction forces, like using the joint movement of flexion or extension or compensating joint reaction force with surrounding soft tissues. Therefore, biomechanical analysis of human ankle joint presented in this study is considered useful for understanding balance control and ankle injury mechanism.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.20 no.2
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• pp.121-128
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• 2011

As high precision industries such as semiconductor, TFT-LCD manufacturing and MEMS continue to grow, the demand for higher DOF precision stages has been increasing. In general, the stages should accommodate a prescribed range of payloads in order to position various precision manufacturing/inspection instruments. Therefore a nonlinear controller using sliding motion is developed, which bears mass perturbation and makes the upper plate of the stage move in 6 DOF. For the application of the nonlinear control, an observer is also developed based on expected noise covariance. To eliminate the steady state error of step response, integral terms are inserted into the state-space model. The linear term of the controller is designed using optimization scheme in which parameters can be weighted according to their physical significance, whereas the nonlinear term of the controller is designed using trial and error method. A comprehensive simulation study proves that the designed controller is robust against mass perturbation and completely eliminates steady state errors.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1999.03b
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• pp.173-178
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• 1999

In this study MD simulations have been performed to observe the behavior of a grain boundary in an a-Fe plate under 2-dimensional loading. In MD simulation the acceleration of every molecule can be achieved from the potential energy and the force interacting between each molecule and the integration of the motion equation by using Verlet method gives the displacement of each molecule. Initially four a-Fe rectangular plates having different misorientation angles of grain boundary were modeled by using the Johnson potential and Morse potential We compared the potential energy of the grain boundary system with that of the perfect structure model. Also we could obtain the width of the grain boundary by investigating the local potential energy distribution. The tensile loading for each grain boundary models was applied and the behavior of grin boundary was studied. From this study it was clarified that in the case using Johnson potential the obvious fracture mechanism occurs along the grain boundary in the case of Morse potential the diffusion of the grain boundary appears instead of the grain boundary fracture.

• Structural Engineering and Mechanics
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• v.90 no.4
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• pp.357-370
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• 2024

Due to the fact that the mechanism of the effects of temperature and initial geometric imperfection on low-velocity impact problem of axially moving plates is not yet clear, the present paper is to fill the gap. In the present paper, the nonlinear dynamic behavior of axially moving imperfect graphene platelet reinforced metal foams (GPLRMF) plates subjected to lowvelocity impact in thermal environment is analyzed. The equivalent physical parameters of GPLRMF plates are estimated based on the Halpin-Tsai equation and the mixing rule. Combining Kirchhoff plate theory and the modified nonlinear Hertz contact theory, the nonlinear governing equations of GPLRMF plates are derived. Under the condition of simply supported boundary, the nonlinear control equation is discretized with the help of Gallekin method. The correctness of the proposed model is verified by comparison with the existing results. Finally, the time history curves of contact force and transverse center displacement are obtained by using the fourth order Runge-Kutta method. Through detailed parameter research, the effects of graphene platelet (GPL) distribution mode, foam distribution mode, GPL weight fraction, foam coefficient, axial moving speed, prestressing force, temperature changes, damping coefficient, initial geometric defect, radius and initial velocity of the impactor on the nonlinear impact problem are explored. The results indicate that temperature changes and initial geometric imperfections have significant impacts.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.380-383
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• 2006

The media transport system is used in a printer, a ATM(Automated Tellor Machine), and so on. The media transport system has many problems through miniaturization and rapid transportation of these machines. In the paper feeding mechanism, it is important to feed the sheet without jamming under any conditions. To avoid sheet jamming, first we need to predict the behavior of the sheet exactly. In this paper, the analysis of media behavior is based on J. Stolte's studies. In all of OA machines, a flexible beam or plate is pushed from the channel. The motion may be constrained by guides. This leads to a transient and geometrically nonlinear problem. The behavior of paper is simulated by dynamic elastica theory. The shape of guide is represented by parametric cubic curve. But J. Stolte's studies did not considered contact condition between sheet and guide. So Klarbring's Model. will be applied. And the analysis of flexible media has to include aerodynamic effect for more exact behavior analysis, because the flexible media can be deformed drastically by a little force. Therefore aerodynamic force must be applied to the governing equation. Lastly, the simulation of this model is performed, and the experiment is performed for verification of this model. The experimental results of low exit velocity are consistent with the simulation results, however experimental results of high exit velocity do not agree well with analytical results. The reason is that there may be other effects like nip Phenomena

• Steel and Composite Structures
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• v.33 no.6
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• pp.891-906
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• 2019

This study considers the instability behavior of sandwich plates considering magnetorheological (MR) fluid core and piezoelectric reinforced facesheets. As facesheets at the top and bottom of structure have piezoelectric properties they are subjected to 3D electric field therefore they can be used as actuator and sensor, respectively and in order to control the vibration responses and loss factor of the structure a proportional-derivative (PD) controller is applied. Furthermore, Halpin-Tsai model is used to determine the material properties of facesheets which are reinforced by graphene platelets (GPLs). Moreover, because the core has magnetic property, it is exposed to magnetic field. In addition, Kelvin-Voigt theory is applied to calculate the structural damping of the piezoelectric layers. In order to consider environmental forces applied to structure, the visco-Pasternak model is assumed. In order to consider the mechanical behavior of structure, sinusoidal shear deformation theory (SSDT) is assumed and Hamilton's principle according to piezoelasticity theory is employed to calculate motion equations and these equations are solved based on differential cubature method (DCM) to obtain the vibration and modal loss factor of the structure subsequently. The effect of different factors such as GPLs distribution, dimensions of structure, electro-magnetic field, damping of structure, viscoelastic environment and boundary conditions of the structure on the vibration and loss factor of the system are considered. In order to indicate the accuracy of the obtained results, the results are validated with other published work. It is concluded from results that exposing magnetic field to the MR fluid core has positive effect on the behavior of the system.

• Steel and Composite Structures
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• v.34 no.2
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• pp.215-226
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• 2020

The aim of this study is to investigate free vibration of functionally graded porous nanocomposite rectangular plates where the internal pores and graphene platelets (GPLs) are distributed in the matrix either uniformly or non-uniformly according to three different patterns. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. The GPL-reinforced plate is modeled using a semi-analytic approach composed of generalized differential quadrature method (GDQM) and series solution adopted to solve the equations of motion. The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and those reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. New results reveal the importance of porosity coefficient, porosity distribution, graphene platelets (GPLs) distribution, geometrical and boundary conditions on vibration behavior of porous nanocomposite plates. It is observed that the maximum vibration frequency obtained in the case of symmetric porosity and GPL distribution, while the minimum vibration frequency is obtained using uniform porosity distribution.

• Steel and Composite Structures
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• v.44 no.2
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• pp.155-169
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• 2022

In the present paper an analytical model was developed to study the non-linear vibrations of Functionally Graded Carbon Nanotube (FG-CNT) reinforced doubly-curved shallow shells using the Multiple Scales Method (MSM). The nonlinear partial differential equations of motion are based on the FGM shallow shell hypothesis, the non-linear geometric Von-Karman relationships, and the Galerkin method to reduce the partial differential equations associated with simply supported boundary conditions. The novelty of the present model is the simultaneous prediction of the natural frequencies and their mode shapes versus different curvatures (cylindrical, spherical, conical, and plate) and the different types of FG-CNTs. In addition to combining the vibration analysis with optimization algorithms based on the genetic algorithm, a design optimization methode was developed to maximize the natural frequencies. By considering the expression of the non-dimensional frequency as an objective optimization function, a genetic algorithm program was developed by valuing the mechanical properties, the geometric properties and the FG-CNT configuration of shallow double curvature shells. The results obtained show that the curvature, the volume fraction and the types of NTC distribution have considerable effects on the variation of the Dimensionless Fundamental Linear Frequency (DFLF). The frequency response of the shallow shells of the FG-CNTRC showed two types of nonlinear hardening and softening which are strongly influenced by the change in the fundamental vibration mode. In GA optimization, the mechanical properties and geometric properties in the transverse direction, the volume fraction, and types of distribution of CNTs have a considerable effect on the fundamental frequencies of shallow double-curvature shells. Where the difference between optimized and not optimized DFLF can reach 13.26%.