Abstract
In dealing with the dynamics of a flexible body, the rigid-body motions and elastic vibrations are analyzed separately. However, rigidbody motions cause vibrations, and elastic vibrations affect rigid-body motions, indicating the inherent coupling between rigid-body motions and elastic vibrations. The coupled equations of motion for a flexible body can be derived by means of Lagrange’s equations in terms of quasi-coordinates. The resulting equations of motion are hybrid and nonlinear. This paper proposes a unified approach for the equations of motion for a flexible body based on the perturbation method and the Lagrange’s equations of motion in terms of quasicoordinates and Euler parameters to analyze a more general case maneuvering. The resulting equations consist of zero-order nonlinear equations of motion which depict rigid-body motions and first-order time-varying linear equations of motion which depict perturbed rigid-body motions and elastic vibration. Hence, the input-shaped maneuvering can be applied to the zero-order equation considering the induced vibrations. Since the input-shaped maneuvering alone cannot achieve vibration suppression, the vibration suppression controller combined with the input-shaped maneuvering is proposed in this study. As a numerical example, a hub with elastic appendages is considered. Numerical results show that the unified modeling approach proposed in this paper is effective in numerical simulation and control design.
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Recommended by Editor Yeon June Kang
Moon K. Kwak received B.S. and M.S. degree in Naval Architecture from Seoul National University in 1981 and 1983. He then received his Ph.D. degree from Virginia Tech in 1989. He is currently a Professor at the Department of Mechanical, Robotics and Energy Engineering of Dongguk University in Seoul, Korea. His research interests are in the area of dynamics and control of flexible multibody system and active vibration control of smart structure.
Dong-Ho Yang received B.S. and M.S. degree in Mechanical Engineering from Dongguk University in 2010 and 2011. He is currently pursuing a Ph.D. Course at the Department of Mechanical, Robotics and Energy Engineering of Dongguk University in Seoul, Korea. His research interests are in the area of dynamics and control of flexible multibody system and active vibration control of smart structure.
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Kwak, M.K., Yang, DH. Dynamic modeling, input-shaped maneuvering and vibration suppression of flexible body using quasi-coordinates and euler parameters. J Mech Sci Technol 27, 657–671 (2013). https://doi.org/10.1007/s12206-013-0115-x
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DOI: https://doi.org/10.1007/s12206-013-0115-x