### Abstract

The objective of this paper is an analytical and numerical study of the dynamics of a beam with attached masses. Specifically, a finite inextensible beam that rests on a uniform elastic foundation and carries an accelerating mass is considered. Of interest is the dynamics of the beam-mass system due to the motion of the moving mass. The influence of various parameters such as forward force, retard force and friction upon the performance of the beam are investigated. The mechanics of the problem is Newtonian. Based on the assumption that when the moving mass is set in motion the mass is assumed to be rolling on the beam, the mechanics, including effects due to friction and convective accelerations of the interface between the moving mass and the beam, are determined. The problem of the system is nonlinear, due to the presence of friction and the convective acceleration. In the modeling, the mass can be accelerated by a force. Meanwhile, the mass is capable of reducing speed and being brought to a stop at any position on the beam by applying a retard force to the mass and/or increasing the friction between the mass and the beam. The force is assumed to be tangential to the deformed configuration of the beam. By employing the Galerkin procedure, the partial differential equations which describe the transient vibrations of the beam-mass system are reduced to an initial value problem with finite dimensions. The method of numerical integration is used to get convergent solutions.

Original language | English |
---|---|

Pages (from-to) | 831-854 |

Number of pages | 24 |

Journal | International Journal of Solids and Structures |

Volume | 35 |

Issue number | 9-10 |

DOIs | |

Publication status | Published - 1998 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Modelling and Simulation
- Materials Science(all)
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics

### Cite this

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**The dynamical analysis of a finite inextensible beam with an attached accelerating mass.** / Wang, Yi-Ming.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The dynamical analysis of a finite inextensible beam with an attached accelerating mass

AU - Wang, Yi-Ming

PY - 1998/1/1

Y1 - 1998/1/1

N2 - The objective of this paper is an analytical and numerical study of the dynamics of a beam with attached masses. Specifically, a finite inextensible beam that rests on a uniform elastic foundation and carries an accelerating mass is considered. Of interest is the dynamics of the beam-mass system due to the motion of the moving mass. The influence of various parameters such as forward force, retard force and friction upon the performance of the beam are investigated. The mechanics of the problem is Newtonian. Based on the assumption that when the moving mass is set in motion the mass is assumed to be rolling on the beam, the mechanics, including effects due to friction and convective accelerations of the interface between the moving mass and the beam, are determined. The problem of the system is nonlinear, due to the presence of friction and the convective acceleration. In the modeling, the mass can be accelerated by a force. Meanwhile, the mass is capable of reducing speed and being brought to a stop at any position on the beam by applying a retard force to the mass and/or increasing the friction between the mass and the beam. The force is assumed to be tangential to the deformed configuration of the beam. By employing the Galerkin procedure, the partial differential equations which describe the transient vibrations of the beam-mass system are reduced to an initial value problem with finite dimensions. The method of numerical integration is used to get convergent solutions.

AB - The objective of this paper is an analytical and numerical study of the dynamics of a beam with attached masses. Specifically, a finite inextensible beam that rests on a uniform elastic foundation and carries an accelerating mass is considered. Of interest is the dynamics of the beam-mass system due to the motion of the moving mass. The influence of various parameters such as forward force, retard force and friction upon the performance of the beam are investigated. The mechanics of the problem is Newtonian. Based on the assumption that when the moving mass is set in motion the mass is assumed to be rolling on the beam, the mechanics, including effects due to friction and convective accelerations of the interface between the moving mass and the beam, are determined. The problem of the system is nonlinear, due to the presence of friction and the convective acceleration. In the modeling, the mass can be accelerated by a force. Meanwhile, the mass is capable of reducing speed and being brought to a stop at any position on the beam by applying a retard force to the mass and/or increasing the friction between the mass and the beam. The force is assumed to be tangential to the deformed configuration of the beam. By employing the Galerkin procedure, the partial differential equations which describe the transient vibrations of the beam-mass system are reduced to an initial value problem with finite dimensions. The method of numerical integration is used to get convergent solutions.

UR - http://www.scopus.com/inward/record.url?scp=0032018733&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032018733&partnerID=8YFLogxK

U2 - 10.1016/S0020-7683(97)00083-8

DO - 10.1016/S0020-7683(97)00083-8

M3 - Article

AN - SCOPUS:0032018733

VL - 35

SP - 831

EP - 854

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

IS - 9-10

ER -