• Structural Engineering and Mechanics
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• v.90 no.6
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• pp.551-568
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• 2024

The present study deals with static and dynamic behaviors including forced vibrations of an elastic rectangular nano plate on the two-parameter foundation. Firstly, the rectangular plate is assumed to be subjected to uniformly distributed and eccentrically applied concentrated loads. The governing equations of the problem are derived by considering the dynamic response of the plate, employing a series of the Chebyshev polynomials for the displacement function and applying the Galerkin method. Then, effects of the non-essential boundary conditions of the plate, i.e., the boundary conditions related to the shearing forces, the bending moments and the corner forces, are included in the governing equation of motion to compensate for the non-satisfied boundary conditions and increase the accuracy of the Galerkin method. The approximate numerical solution is accomplished using an iterative process due to the non-linearity of the unilateral property of the two-parameter foundation. The plate under static concentrated load is investigated in detail numerically by considering a wide range of parameters of the plate and the foundation stiffnesses. Numerical treatment of the problem in the time domain is carried out by assuming a stepwise variation of the concentrated load and the linear acceleration procedure is employed in the solution of the system of governing differential equations derived from the equation of motion. Time variations of the contact region and those of the displacements of the plate are presented in the figures for various numbers of the two-parameter of the foundation, as well as the classical and nano parameters of the plate particularly focusing on the non-linearity of the problem due to the plate lift-off from the unilateral foundation. The effects of classical and nonlocal parameters and loading are investigated in detail. Definition of the separation between the plate and the two-parameter foundation is presented and applied to the given problem. The effect of the lift-off on the static and dynamic behavior of the rectangular plate is studied in detail by considering various loading conditions. The numerical study shows that the effect of nonlocal parameters on the behavior of the plate becomes significant, when nonlinearity becomes more profound, due to the lift-off of the plate. It is seen that the size effects are significant in static and dynamic analysis of nano-scaled rectangular plates and need to be included in the mechanical analyses. Furthermore, the corner displacement of the plate is affected more significantly from the lift-off, whereas it is less marked in the time variation of the middle displacement of the plate. Several numerical examples are presented to examine the sensibility of various parameters associated with nonlocal parameters of the plate and foundation. Both stiffening and softening nonlocal parameters behavior of the plate are identified in the numerical solutions which show that increasing the foundation stiffness decreases the extent of the contact region, whereas the stiffness of the shear layer increases the contact region and reduces the foundation settlement considerably.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.700-703
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• 1997

A robust controller for a 6 DOF magnetically levitated fine manipulator is presented. The proposed controller consists of following two parts : a model reference controller (MRC) and a H$_{\infty}$ controller (HIC). First, the MRC stabilizes the motion of the manipulator. Then, the motion of the manipulator follows that of the reference model. Second, the HIC minimizes errors generated from the MRC due to noise and disturbance since the HIC is a kind of robust controller. The experiments of position control and tracking control are carried out by use of the proposed controller under the conditions of free disturbances and forced disturbances. Also, the experiments using PID controller are carried out under the same conditions. The results from above two controllers are compared to investigate the control performances. As the results, it is observed that the proposed controller has similar position accuracy but better tracking performances comparing to the PID controller as well as good disturbance rejection effect due to the robust characteristics of the controller. In conclusion, it is verified that the proposed controller has the simple control structure, the good tracking performances and good disturbance rejection effect due to the robust characteristics of the controller..

• Structural Engineering and Mechanics
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• v.34 no.4
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• pp.507-523
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• 2010

Parametric and forced non-linear vibrations of an axially moving rotor both in non-resonance and near-resonance cases have been investigated analytically in this paper. The axial speed is assumed to involve a mean value along with small harmonic fluctuations. Hamilton's principle is employed for this gyroscopic system to derive three coupled non-linear equations of motion. Longitudinal inertia is neglected under the quasi-static stretch assumption and two integro-partial-differential equations are obtained. With introducing a complex variable, the equations of motion is presented in the form of a single, complex equation. The method of multiple scales is applied directly to the resulting equation and the approximate closed-form solution is obtained. Stability boundaries for the steady-state response are formulated and the frequency-response curves are drawn. A number of case studies are considered and the numerical simulations are presented to highlight the effects of system parameters on the linear and nonlinear natural frequencies, mode shapes, limit cycles and the frequency-response curves of the system.

• Wind and Structures
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• v.25 no.1
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• pp.25-38
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• 2017

This study investigates the dynamic analysis of a transversely isotropic thin plate. The plate is made of hyperelastic John's material and its constitutive law is obtained by taken the Frechect derivative of the highlighted energy function with respect to the geometry of deformation. The three-dimensional equation governing the motion of the plate is expressed in terms of first Piola-Kirchhoff's stress tensor. In the reduction to an equivalent two-dimensional plate equation, the obtained model generalizes the classical plate equation of motion. It is obtained that the plate under consideration exhibits harmonic force within its planes whereas this force varnishes in the classical plate model. The presence of harmonic forces within the planes of the considered plate increases the natural and resonance frequencies of the plate in free and forced vibrations respectively. Further, the parameter characterizing the transversely isotropic structure of the plate is observed to increase the plate flexural rigidity which in turn increases both the natural and resonance frequencies. Finally, this study reinforces the view that non-classical models of problems in elasticity provide ample opportunity to reveal important phenomena which classical models often fail to apprehend.

• Structural Engineering and Mechanics
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• v.68 no.3
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• pp.359-368
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• 2018

This paper deals with the dynamic stability of nanocomposite pipes conveying pulsating ferrofluid. The pipe is reinforced by carbon nanotubes (CNTs) where the agglomeration of CNTs are considered based on Mori-Tanaka model. Due to the existence of CNTs and ferrofluid flow, the structure and fluid are subjected to axial magnetic field. Based on Navier-Stokes equation and considering the body forced induced by magnetic field, the external force of fluid to the pipe is derived. For mathematical modeling of the pipe, the first order shear deformation theory (FSDT) is used where the energy method and Hamilton's principle are used for obtaining the motion equations. Using harmonic differential quadrature method (HDQM) and Bolotin's method, the motion equations are solved for calculating the excitation frequency and dynamic instability region (DIR) of the structure. The influences of different parameters such as volume fraction and agglomeration of CNTs, magnetic field, structural damping, viscoelastic medium, fluid velocity and boundary conditions are shown on the DIR of the structure. Results show that with considering agglomeration of CNTs, the DIR shifts to the lower excitation frequencies. In addition, the DIR of the structure will be happened at higher excitation frequencies with increasing the magnetic field.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.11
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• pp.1049-1055
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• 2008

Modern multidisciplinary computational fluid dynamics often incorporates moving boundaries, as would be required in the applications such as design optimization, aeroelasticity, or forced boundary motion. It is challenging to develop robust, efficient grid deformation algorithms when large displacement of the moving boundaries is required. In this paper, a volume grid deformation code is developed based on the finite macro-element and the transfinite Interpolation, and then interfaces to a structured multi-block Navier-Stokes in-house code. As demonstrated by an airfoil with pitching motion, the hysteresis loops of lift, drag and moment coefficients of the developed method are shown to be in good agreement with those of experimental data.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.6
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• pp.793-803
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• 1997

This experimental study was mainly investigated on the swirl flow characteristics in the cylinder generated by a helical intake port. LDA system was used for the measurement of in-cylinder velocity fields. Tangential and axial velocity profiles, with varying valve lifts, valve eccentricity ratios and axial distance, were measured. When the intake valve was set in the cylinder center, we could find that in-cylinder swirl flow fields were composed of a forced vortex motion and a free vortex motion in the vicinity of the cylinder center and the cylinder wall respectively. In case of valve eccentricity ratio, N$_{y}$ = 0.45, the vortex flow which rotates to the opposite direction of a main rotating flow in the cylinder was found. And the reverse flow toward the cylinder head surface was also found in axial velocity profile and it showed the tendency of the linear decrease in the region of 0.leq.Y/B.leq.1.2.2.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.19 no.7
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• pp.98-105
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• 2020

This study deals with the passive control of the dynamic characteristics of a theoretical model which is a string with fixed ends and loaded by two point masses - a main mass (M_o) and a secondary mass (M_s). It has been controlled passively by means of a relocation of a secondary mass. A main mass placed on the string is considered as a vibrating receiver which be forced to vibrate by a vibrating source being positioned on the string. By analyzing the motion of a string, the equation of motion for a string was derived by using a method of variation of parameters. To define the optimal conditions for the vibration reduction, the governing equation, which denotes the dynamic response of a string was derived in the closed form and then evaluated numerically. The possibility of reduction of an amplitude and a power being transmitted to a main mass were found to depend on the location and the magnitude of a secondary mass as well as the range of a forcing frequency.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.5 s.98
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• pp.58-65
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• 1999

A magnetic levitation system requires a robustness to overcome a dynamic instability due to disturbances. In this paper a robust controller for a magnetically levitated fine manipulator is presented. The proposed controller consists of following two parts: a model reference controller and an $H_{\infty}$ controller. First, the model reference control stabilizes the motion of the manipulator. Then, the motion of the manipulator follows that of the reference model. Second, the $H_{\infty}$ control minimizes errors generated from the model reference control due to noise and disturbance since the $H_{\infty}$ control is a kind of robust control. The experiments of position control and tracking control are carried out by use of the proposed controller under the conditions of free disturbances and forced disturbances. Also, the experiments using PID controller are carried out under the same conditions. The results from above two controllers are compared to investigate the control performances. As the results, it is observed that the proposed controller has similar position accuracy but better tracking performances comparing to the PID controller as well as good disturbance rejection effect due to the robust characteristics of the controller. In conclusion. it is verified that the proposed controller has the simple control structure, the good tracking performances and good disturbance rejection effect due to the robust characteristics of the controller.

• Journal of Advanced Marine Engineering and Technology
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• v.33 no.6
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• pp.867-872
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• 2009

In centrifugal oil filters particles are forced to move toward the filter casing wall by centrifugal force in the rotating oil flow and the particles are trapped and removed on the filter paper installed at the wall. In the present study, flow field of oil and particle motion in a centrifugal oil filter has been numerically calculated in order to estimate the filtering efficiency for various operating conditions. Fluent code was used for the numerical calculations. Uncoupling the oil flow and the particle motion and the use of particle tracking trajectory enabled the estimation of filtering efficiency for various particle sizes, particle density and the filter rotational speed. Higher filtering efficiency was observed for heavier and larger particles as well as higher filter rotational speed. For the typical case of the particle density of $6000kg/m^3$ and the particle size of $10{\mu}m$ at 3500 RPM, the calculated filtering efficiency per passage was 0.31.