• Structural Engineering and Mechanics
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• v.86 no.3
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• pp.361-371
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• 2023

Boundary condition is an important factor affecting the vibration characteristics of structures, under different boundary conditions, structures will exhibit different vibration behaviors. On the basis of the previous work, this paper extends to the nonlinear resonance behavior of axially moving graphene platelets reinforced metal foams (GPLRMF) plates with geometric imperfection under different boundary conditions. Based on nonlinear Kirchhoff plate theory, the motion equations are derived. Considering three boundary conditions, including four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS), the nonlinear ordinary differential equation system is obtained by Galerkin method, and then the equation system is solved to obtain the nonlinear ordinary differential control equation which only including transverse displacement. Subsequently, the resonance response of GPLRMF plates is obtained by perturbation method. Finally, the effects of different boundary conditions, material properties (including the GPLs patterns, foams distribution, porosity coefficient and GPLs weight fraction), geometric imperfection, and axial velocity on the resonance of GPLRMF plates are investigated.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.1
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• pp.61-68
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• 1991

The system such as railway bridge can be modelled as the restrained beam with intermediate supports. This kind of structures are subject to the moving load, which has a great effect on dynamic stresses and can cause sever motions, especially at high velocities. Therefore, to analyze the dynamic characteristics of the system due to the moving load is very important. In this paper, the governing equation of motion of a restrained beam subjected to the moving load is derived by using the Hamilton's principle. The orthogonal polynomial functions, which are trial functions and satisfying the geometric and dynamic boundary conditions, are obtained through simple procedure. The dynamic response of the system subjected to the moving loads is obtained by using the Galerkin's method and the numerical time integration technique. The numerical tests for various constraint, velocity and boundary conditions were preformed. Furthermore, the effects of mass of the moving load are studied in detail.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.4
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• pp.315-322
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• 2009

This paper presents a novel numerical method based on the extended moving least squares finite difference method(MLS FDM) for solving 1-D Stefan problem. The MLS FDM is employed for easy numerical modelling of the moving boundary and Taylor polynomial is extended using wedge function for accurate capturing of interfacial singularity. Difference equations for the governing equations are constructed by implicit method which makes the numerical method stable. Numerical experiments prove that the extended MLS FDM show high accuracy and efficiency in solving semi-infinite melting, cylindrical solidification problems with moving interfacial boundary.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.86-87
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• 2003

Unstructured grid system is suitable for flows of complex geometries. For problems with moving boundary walls, the grid system must be changed and deformed with time if we use a body fitted grid system. In this paper, a new moving-grid finite-volume method on unstructured grid system is proposed and developed for unsteady compressible flows with shock waves. To assure geometric conservation laws on moving grid system, a control volume on the space-time unified domain is adopted for estimating numerical flux. The method is described and applied for two-dimensional flows.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.38.1-38
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• 2001

In this paper, the vibration suppression problem of an axially moving power transmission belt is investigated. The equations of motion of the moving belt is first derived by using Hamilton´s principle for systems with changing mass. The total mechanical energy of the belt system is considered as a Lyapunov function candidate. Using the Lyapunov second method, a nonlinear boundary control law that guarantees the uniform asymptotic stability is derived. The control performance with the proposed control law is simulated. It is shown that a boundary control can still achieve the uniform stabilization for belt systems.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.342-347
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• 2003

In this paper, an active vibration control of a translating tensioned string with the use of an electro-hydraulic servo mechanism at the right boundary is investigated. The dynamics of the moving strip is modeled as a string with tension by using Hamilton’s principle for the systems with changing mass. The control objective is to suppress the transverse vibrations of the strip via boundary control. A right boundary control law in the form of current input to the servo valve based upon the Lyapunov’s second method is derived. It is revealed that a time-varying boundary force and a suitable passive damping at the right boundary can successfully suppress the transverse vibrations. The exponential stability of the closed loop system is proved. The effectiveness of the control laws proposed is demonstrated via simulations.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.6
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• pp.619-627
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• 2004

In most industrial applications, the geometrical complexity is combined with the moving boundaries. These problems considerably increase the computational difficulties since they require, respectively, regeneration and deformation of the grid. As a result, engineering flow simulation is restricted. In order to solve this kind of problems the immersed boundary method was developed. In this study, the immersed boundary method is applied to the numerical simulation of stationary, rotating and oscillating cylinders in the 2-dimensional square cavity. No-slip velocity boundary conditions are given by imposing feedback forcing term to the momentum equation. Besides, this technique is used with a second-order accurate interpolation scheme in order to improve the accuracy of flow near the immersed boundaries. The governing equations for the mass and momentum using the immersed boundary method are discretized on the non-staggered grid by using the finite volume method. The results agree well with previous numerical and experimental results. This study presents the possibility of the immersed boundary method to apply to the complex flow experienced in the industrial applications. The usefulness of this method will be confirmed when we solve the complex geometries and moving bodies.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.5
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• pp.439-446
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• 2012

This paper presents an implicit moving least squares(MLS) difference method for improving the solution accuracy of 1-D free boundary problems, which implicitly updates the topology change of moving interface. The conventional MLS difference method explicitly updates the moving interface; it requires no iterative solution procedure but results in the loss of accuracy. However, the newly developed implicit scheme makes the total system nonlinear involving iterative solution procedure, but numerical verification show that it dramatically elevates the solution accuracy with moderate computation increase. Through numerical experiments for melting problems having moving singularity, it is verified that the proposed method can achieve the second order accuracy.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.11
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• pp.895-903
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• 2007

CMBT(Curved Moving Boundary Treatment) is a newly developed scheme for the treatment of a no slip condition on the curved solid wall of moving obstacle in a flow field. In our research CMBT was used to perform LBM simulation of a flow over a moving circular cylinder to determine the flow feature and aerodynamics characteristic of the cylinder. To ascertain the applicability of CMBT on the complex shape of the obstacle, it was first simulated for the case of the flow over a fixed circular cylinder in a channel and the results were compared against the solution of Navier-Stokes equation with deforming mesh technique. The simulations were performed in a moderate range of reynolds number at each moving cylinder to identify the flow feature and aerodynamic characteristics of circular cylinder in a channel. The drag coefficients of the cylinder were calculated from the simulation results. We have numerically confirmed that the critical reynolds number for vortex shedding is ar Re=250 and the result is the same as the case of fixed cylinder. As the cylinder approaching to one wall, the 2nd vortex is developed by interacting with the wall boundary-layer vorticity. As the velocity ratio increase the third vortex are generated by interacting with the 2nd vortexes developed on the upper and lower wall boundary layer. The resultant $C_d$ decrease as reynolds number increasing and the Cd approached to a value when Re>1000.

• International Journal of Control, Automation, and Systems
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• v.2 no.1
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• pp.55-67
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• 2004

In this paper, an active vibration control of a translating steel strip in a zinc galvanizing line is investigated. The control objectives in the galvanizing line are to improve the uniformity of the zinc deposit on the strip surfaces and to reduce the zinc consumption. The translating steel strip is modeled as a moving belt equation by using Hamilton’s principle for systems with moving mass. The total mechanical energy of the strip is considered to be a Lyapunov function candidate. A nonlinear boundary control law that assures the exponential stability of the closed loop system is derived. The existence of a closed-loop solution is shown by proving that the closed-loop dynamics is dissipative. Simulation results are provided.