• Journal of KSNVE
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• v.10 no.1
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• pp.138-143
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• 2000

Longitudinal vibration of an axially moving material is investigated by using the assumed modes method. To circumvent a difficulty in choosing the comparison functions which satisfy the boundary conditions, the assumed modes method is adopted by which equations of motion are discretized. Based on the discretized equations, the complex eigenvalue problem is solved and then the effects of the translating velocity on the natural frequencies and modes are analyzed.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.619-624
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• 2000

Longitudinal vibration of an axially moving material is investigated by using the assumed modes method. to circumvent a difficulty in choosing the comparison functions which satisfy the boundary conditions the assumed modes method is adopted by which equations of motion are discretized. Based on the discretized equations, the complex eigenvalue problem is solved and then the effects of the translating velocity on the natural frequencies and modes are analyzed.

• Steel and Composite Structures
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• v.42 no.5
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• pp.649-655
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• 2022

In presented paper, moving load problem of simply supported axially functionally graded (AFG) beam is investigated under temperature rising based on the first shear beam theory. The material properties of beam vary along the axial direction. Material properties of the beam are considered as temperature-dependent. The governing equations of problem are derived by using the Lagrange procedure. In the solution of the problem the Ritz method is used and algebraic polynomials are used with the trivial functions for the Ritz method. In the solution of the moving load problem, the Newmark average acceleration method is used in the time history. In the numerical examples, the effects of material graduation, temperature rising and velocity of moving load on the dynamic responses ofAFG beam are presented and discussed.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.2707-2712
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• 2003

In this paper, with the utilization of a three-dimensional version of Leibniz’s rule, the procedure of deriving the time rate of change of an energy functional for axially moving continua is investigated. It will be shown that the method in [14], which describes the way of getting the time rate of change of an energy functional in Eulerian description, and subsequent results in [10, 11] are not complete. The key point is that the time derivatives at boundaries in the Eulerian description of axially moving continua should take into account the velocity of the moving material itself. A noble way of deriving the time rate of change of the energy functional is proposed. The correctness of the proposed method has been confirmed by other approaches. Two examples, one-dimensional axially moving string and beam equations, are provided for the purpose of demonstration. The results following the procedure proposed and the results in [14] are compared.

• Structural Engineering and Mechanics
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• v.53 no.5
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• pp.981-995
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• 2015

This paper presents a finite element procedure for dynamic analysis of non-uniform Timoshenko beams made of axially Functionally Graded Material (FGM) under multiple moving point loads. The material properties are assumed to vary continuously in the longitudinal direction according to a predefined power law equation. A beam element, taking the effects of shear deformation and cross-sectional variation into account, is formulated by using exact polynomials derived from the governing differential equations of a uniform homogenous Timoshenko beam element. The dynamic responses of the beams are computed by using the implicit Newmark method. The numerical results show that the dynamic characteristics of the beams are greatly influenced by the number of moving point loads. The effects of the distance between the loads, material non-homogeneity, section profiles as well as aspect ratio on the dynamic responses of the beams are also investigated in detail and highlighted.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.164-168
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• 2004

The vibration analysis of an axially moving membrane are investigated when the membrane has the two sets of in-plane boundary conditions, which are free and fixed constraints in the lateral direction. Since the in-plane stiffness is much higher than the out-of-plane stiffness, it is assumed during deriving the equations of motion that the in-plane motion is in a steady state. Under this assumption. the equation of out-of\ulcornerplane motion is derived, which is a linear partial differential equation influenced by the in-plane stress distributions. After discretizing the equation by using the Galerkin method, the natural frequencies and mode shapes are computed. In particular, we put a focus on analyzing the effects of the in-plane boundary conditions on the natural frequencies and mode shapes of the moving membrane.

• 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.910-918
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• 2004

The vibration analysis of an axially moving membrane are investigated when the membrane has the two sets of in-plane boundary conditions, which are free and fixed constraints in the lateral direction. Since the in-plane stiffness is much higher than the out-of-plane stiffness, it is assumed during deriving the equations of motion that the in-plane motion is in a steady state. Under this assumption, the equation of out-of-plane motion is derived, which is a linear partial differential equation influenced by the in-plane stress distributions. After discretizing the equation by using the Galerkin method, the natural frequencies and mode shapes are computed. In particular, we put a focus on analyzing the effects of the in-plane boundary conditions on the natural frequencies and mode shapes of the moving membrane.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.3
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• pp.221-227
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• 2002

The longitudinal and lateral in-plane vibrations of an axially moving membrane are investigated when the membrane has translating acceleration. By extended Hamilton's principle, the governing equations are derived. The equations of motion for the in-plane vibrations are linear and coupled. These equations are discretized by using the Galerkin approximation method after they are transformed into the variational equations, j.e., the weak forms so that the admissible functions can be used for the bases of the in-plane deflections. With the discretized equations for the in-plane vibrations, the natural frequencies and the time histories of the deflections are obtained.

• Journal of KSNVE
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• v.10 no.5
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• pp.838-842
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• 2000

The vibration of an axially moving string is studied when the string has geometric non-linearity and translating acceleration. Based upon the von karman strain theory, the equations of motion are derived considering the longitudinal and transverse deflection. The equation for the longitudinal vibration is linear and uncoupled, while the equation for the transverse vibration is non-linear and coupled between the longitudinal and transverse deflections. These equations are discretized by using the Galerkin approximation after they are transformed into the variational equations, i.e. the weak forms so that the admissible and comparison functions can be used for the bases of the longitudinal and transverse deflections respectively. With the discretized nonlinear equations, the time responses are investigated by using the generalized-$\alpha$ method.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.613-617
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• 2001

The longitudinal vibration of an axially moving membrane is studied when the membrane has translating acceleration. The equation for the longitudinal vibration is linear and coupled, The equation for the longitudinal vibration are discretized by using the Galerkin approximation after they are transformed into the variational equations, i.e., the weak forms so that the admissible function can be used for the bases of the longitudinal deflection. With the discretized equations for the longitudinal vibration, the time responses are investigated by using newmark method.