### Abstract

Asymptotic behavior of the solution of the moving oscillator problem is examined for large values of the spring stiffness for the general case of nonzero beam initial conditions. In the limit of infinite spring stiffness, the moving oscillator problem for a simply supported beam is shown to be not equivalent in a strict sense to the moving mass problem; i.e., beam displacements obtained by solving the two problems are the same, but the higher-order derivatives of the two solutions are different. In the general case, the force acting on the beam from the oscillator is shown to contain a high-frequency component, which does not vanish, or even grows, when the spring coefficient tends to infinity. The magnitude of this force and its dependence on the oscillator parameters can be estimated by considering the asymptotics of the solution for the initial stage of the oscillator motion. For the case of a simply supported beam, the magnitude of the high-frequency force linearly depends on the oscillator eigenfrequency and velocity. The deficiency of the moving mass model is noted in that it fails to predict stresses in the bridge structure. Results of numerical experiments are presented.

Original language | English (US) |
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Pages | 1845-1854 |

Number of pages | 10 |

State | Published - Dec 1 2001 |

Event | 18th Biennial Conference on Mechanical Vibration and Noise - Pittsburgh, PA, United States Duration: Sep 9 2001 → Sep 12 2001 |

### Other

Other | 18th Biennial Conference on Mechanical Vibration and Noise |
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Country | United States |

City | Pittsburgh, PA |

Period | 9/9/01 → 9/12/01 |

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### ASJC Scopus subject areas

- Modeling and Simulation
- Mechanical Engineering
- Computer Science Applications
- Computer Graphics and Computer-Aided Design

### Cite this

*On equivalence of the moving mass and moving oscillator problems*. 1845-1854. Paper presented at 18th Biennial Conference on Mechanical Vibration and Noise, Pittsburgh, PA, United States.