• Journal of the Korean Society for Precision Engineering
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• v.28 no.8
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• pp.959-965
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• 2011

This paper presents the dynamic modeling and vibration suppression methods for axially deploying beams subjected to gravity. A modal modeling method is employed to develop the lateral vibration model for axially deploying beams. Simulation is made to validate the proposed model as well as to investigate the dynamics of axially deploying beams. This paper rigorously investigates the gravity effect as a source of vibration for axially deploying beams. In order to suppress lateral vibration for deploying beams, the moving speed command is modified by using the input shaping method, Experiments are also performed to prove the proposed vibration suppression method. The simulations and experiments show that the proposed modeling and input shaping methods are effective for the dynamic analysis and vibration suppression of axially deploying beams subjected to gravity.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.21 no.2
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• pp.202-207
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• 2012

Multi-stage deploying beams are useful for transporting parts or products handling in production lines. However, such multi-stage beams are often exposed to unwanted vibration due to the presence of their flexibility and time-varying properties. This paper is concerned with dynamic modeling and analysis of 2-stage axially deploying beams under gravity by using the finite element method. A variable domain finite element method is employed to develop the dynamic model. A rigorous method to account for engagement of two-stage beams during the deploying procedure is introduced by breaking the entire domain into three variable domains. Several deploying strategies are tested to analyze the residual vibrations. Several examples are illustrated to investigate the self-induced damping and the effects of deploying strategy on the vibrations.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2013.05a
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• pp.407-408
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• 2013

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.24 no.11
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• pp.898-906
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• 2014

This paper presents a reduction method for a straight-line path error of a flexible beam deploying from a rotating rigid hub. Previous studies discussed about only vibration phenomena of flexible beams deploying from rotating hubs; however, this study investigates a vibration reduction of a rotating beam with variable length. The equation of motion and associated boundary conditions are derived for a flexible beam deploying from a rotating rigid hub, and then they are transformed to a variational equation. By applying the Galerkin method, the discretized equations are obtained from the variational equation. Based on the discretized equations, the dynamic responses of a rotating/deploying beam are analyzed when the beam end has a straight line motion. A reduction method for the trajectory error is proposed, using the average length of a rotating/deploying beam. It is shown that the proposed method is able to reduce the residual vibration of a rotating/deploying beam.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.12
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• pp.874-880
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• 2015

This paper presents the vibration analysis of a deploying beam with spin when the beam has a time-dependent spinning speed. In the previous studies for the deploying beams with spin, the spinning speed was time-independent. However, it is more reasonable to consider the time-dependent spinning speed. The present study introduces the time-dependent spinning speed in the modeling. The Euler-Bernoulli beam theory and von Karman nonlinear strain theory are used together to derive the equations of motion. After the equations of motion are transformed into the weak forms, the weak forms are discretized. The natural frequency and dynamic response are obtained. The effect of the time-dependent spinning speed on the dynamic response is studied.

• Structural Engineering and Mechanics
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• v.86 no.3
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• pp.291-309
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• 2023

This paper addresses the finite element modeling of functionally graded porous (FGP) beams for free vibration and buckling behaviour cases. The formulated finite element is based on simple and efficient higher order shear deformation theory. The key feature of this formulation is that it deals with Euler-Bernoulli beam theory with only three unknowns without requiring any shear correction factor. In fact, the presented two-noded beam element has three degrees of freedom per node, and the discrete model guarantees the interelement continuity by using both C⁰ and C¹ continuities for the displacement field and its first derivative shape functions, respectively. The weak form of the governing equations is obtained from the Hamilton principle of FGP beams to generate the elementary stiffness, geometric, and mass matrices. By deploying the isoparametric coordinate system, the derived elementary matrices are computed using the Gauss quadrature rule. To overcome the shear-locking phenomenon, the reduced integration technique is used for the shear strain energy. Furthermore, the effect of porosity distribution patterns on the free vibration and buckling behaviours of porous functionally graded beams in various parameters is investigated. The obtained results extend and improve those predicted previously by alternative existing theories, in which significant parameters such as material distribution, geometrical configuration, boundary conditions, and porosity distributions are considered and discussed in detailed numerical comparisons. Determining the impacts of these parameters on natural frequencies and critical buckling loads play an essential role in the manufacturing process of such materials and their related mechanical modeling in aerospace, nuclear, civil, and other structures.