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| Giampaolo Zen (MS, August 2004) |
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| Current address: |
| Progettazione motore |
| FERRARI GESTIONE SPORTIVA |
| 55/57 via Ascari, 41053 Maranello (M), Italy |
| e-mail: gzen@ferrai.it |
| Friction induced transverse vibrations of an axially accelerating continuum |
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The purpose of this thesis is to investigate the dynamic response of axially translating continua subjected to the combined effects of a stationary friction load and axial acceleration; such systems are both non-conservative and gyroscopic. The continuum is modeled as a tensioned string translating between two rigid supports with a time dependent velocity profile; the point load acting on the system is considered to be stationary and elastically supported.
The equations of motions are derived with the extended Hamilton’s principle and discretized in the space domain with the finite element method. The lateral response and the stability of the system are then analyzed with both implicit and explicit numerical methods; the Floquet theory is employed for the linear case, while an adaptive step Runge-Kutta algorithm is used when the equation becomes non-linear.
Results are given in the form of time history diagrams and instability point grids for different sets of parameters such as stationary load location, stiffness of the elastic support, initial tension, friction coefficient and velocity profile. Numerical results for simplified cases are also presented in order to give a comparison with previous studies.
The practical case of an axially translating magnetic tape is eventually analyzed. The description of the experimental equipment that could be used to directly measure the oscillations in the tape drive is also given in the appendix.
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