### Abstract

The objective of this paper is to present analytical and numerical methodologies to evaluate the transient dynamics of a moving mass rolling on an eccentric path along a finite simple-supported inextensible beam. The eccentric path of a beam exists due to either manufacturing imperfection or preset purpose to produce specified dynamic characteristics to satisfy special performances. The eccentricity of the eccentric path may have different shapes and is assumed to be a spatial variable which is the distance from the neutral axis of the beam to the path. The method used in the analysis is Newtonian. The mechanics of the interface between the moving mass and the beam is determined by modeling the mass as a rigid body that is rolling on the eccentric axis when the mass is set on motion; moment of the moving mass acting on the beam along the eccentric path is taken into account. Based on EulerBernoulli beam theory and inextensibility constraint, the mechanics, including effects due to friction and convective accelerations, of the interface between the mass and the beam is obtained. By employing Galerkin's procedure to eliminate spatial dependence, the problem reduces to a multi-degrees-of-freedom dynamical system with time dependent coefficients. Result of present study indicates that the eccentricity of eccentric path plays an important role to the dynamics of a beam-mass system. If the shape of the eccentric path is concave upward, the amplitude of eccentricity amplifies not only the positive amplitude of the trajectory of mass but also the negative displacement of the beam even if the amplitude of eccentricity is tiny. However, if the shape of the eccentric path is convex upward, the amplitude of eccentricity attenuated the displacement of the beam. In addition, it is generally true that as the mass moves from the left end, the occurrence of negative displacement exists when the mass is subjected by a reverse force and approaches to the right terminal.

Original language | English |
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Pages (from-to) | 118-128 |

Number of pages | 11 |

Journal | International Journal of Mechanical Sciences |

Volume | 55 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 Feb 1 |

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### All Science Journal Classification (ASJC) codes

- Civil and Structural Engineering
- Materials Science(all)
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

### Cite this

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**The transient dynamics of a moving mass traveling on an eccentric path along a finite simple supported inextensible beam.** / Wang, Yi Ming; Chen, Chung Hsien.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The transient dynamics of a moving mass traveling on an eccentric path along a finite simple supported inextensible beam

AU - Wang, Yi Ming

AU - Chen, Chung Hsien

PY - 2012/2/1

Y1 - 2012/2/1

N2 - The objective of this paper is to present analytical and numerical methodologies to evaluate the transient dynamics of a moving mass rolling on an eccentric path along a finite simple-supported inextensible beam. The eccentric path of a beam exists due to either manufacturing imperfection or preset purpose to produce specified dynamic characteristics to satisfy special performances. The eccentricity of the eccentric path may have different shapes and is assumed to be a spatial variable which is the distance from the neutral axis of the beam to the path. The method used in the analysis is Newtonian. The mechanics of the interface between the moving mass and the beam is determined by modeling the mass as a rigid body that is rolling on the eccentric axis when the mass is set on motion; moment of the moving mass acting on the beam along the eccentric path is taken into account. Based on EulerBernoulli beam theory and inextensibility constraint, the mechanics, including effects due to friction and convective accelerations, of the interface between the mass and the beam is obtained. By employing Galerkin's procedure to eliminate spatial dependence, the problem reduces to a multi-degrees-of-freedom dynamical system with time dependent coefficients. Result of present study indicates that the eccentricity of eccentric path plays an important role to the dynamics of a beam-mass system. If the shape of the eccentric path is concave upward, the amplitude of eccentricity amplifies not only the positive amplitude of the trajectory of mass but also the negative displacement of the beam even if the amplitude of eccentricity is tiny. However, if the shape of the eccentric path is convex upward, the amplitude of eccentricity attenuated the displacement of the beam. In addition, it is generally true that as the mass moves from the left end, the occurrence of negative displacement exists when the mass is subjected by a reverse force and approaches to the right terminal.

AB - The objective of this paper is to present analytical and numerical methodologies to evaluate the transient dynamics of a moving mass rolling on an eccentric path along a finite simple-supported inextensible beam. The eccentric path of a beam exists due to either manufacturing imperfection or preset purpose to produce specified dynamic characteristics to satisfy special performances. The eccentricity of the eccentric path may have different shapes and is assumed to be a spatial variable which is the distance from the neutral axis of the beam to the path. The method used in the analysis is Newtonian. The mechanics of the interface between the moving mass and the beam is determined by modeling the mass as a rigid body that is rolling on the eccentric axis when the mass is set on motion; moment of the moving mass acting on the beam along the eccentric path is taken into account. Based on EulerBernoulli beam theory and inextensibility constraint, the mechanics, including effects due to friction and convective accelerations, of the interface between the mass and the beam is obtained. By employing Galerkin's procedure to eliminate spatial dependence, the problem reduces to a multi-degrees-of-freedom dynamical system with time dependent coefficients. Result of present study indicates that the eccentricity of eccentric path plays an important role to the dynamics of a beam-mass system. If the shape of the eccentric path is concave upward, the amplitude of eccentricity amplifies not only the positive amplitude of the trajectory of mass but also the negative displacement of the beam even if the amplitude of eccentricity is tiny. However, if the shape of the eccentric path is convex upward, the amplitude of eccentricity attenuated the displacement of the beam. In addition, it is generally true that as the mass moves from the left end, the occurrence of negative displacement exists when the mass is subjected by a reverse force and approaches to the right terminal.

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U2 - 10.1016/j.ijmecsci.2012.01.005

DO - 10.1016/j.ijmecsci.2012.01.005

M3 - Article

AN - SCOPUS:84862807851

VL - 55

SP - 118

EP - 128

JO - International Journal of Mechanical Sciences

JF - International Journal of Mechanical Sciences

SN - 0020-7403

IS - 1

ER -