Some Aspects Concerning the Vibrations of a Nonlinear Mechanical System with a Medical Device
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Abstract
In this paper, some problems about the parameters of the vibrations (periods, amplitudes, and mean value) for one mechanical system housing a medical device are discussed. The system is acted upon by an earthquake for a certain period, then oscillates freely. The study focuses on both the vibrations during the earthquake and the free oscillations. In addition, the medical device cannot be separated from the last (the third) shell; that is, there exists no motion between this last shell and the medical device. The limitations are determined by the amplitudes, velocities, and accelerations of the medical device's vibrations. The elastic forces in the system are nonlinear. The vibrations are small, so the classical approximation applies. The analytical solution of the equations of motion is also described for a particular case of motion, as well as for the case of an earthquake. The system is considered to have only two degrees of freedom, the vertical displacements of the shells. The analytical solution is obtained using the multiple-scales method. The situations in which the resonance appears are also presented. Some results of the numerical study are also presented. A numerical study shows that rotational displacements have a small influence on the characteristics of the vertical displacement. The influence of different parameters is also highlighted.
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