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Rheological-dynamical Analogy: Frequency Dependence of the System Parameters of Internally Damped Bars

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An analytical rheological-dynamical visco-elastic solution of one-dimensional longitudinal continuous vibration of bars has been developed and used to evaluate the validity of the classical analytical elastic solutions. As it is well known, the resonance occurs only in the continuous or single-degree-of-freedom ideal elastic system when the excitation frequency ωP is equal to the one of the natural frequency of the bar. However, owing to the visco-elastic nature of materials and frequency dependence of the damping factor ζ it is useful to consider separately the situations arising when the ζ is positive (system is stable) and when it is negative. Negative damping factor means that the complementary solution of the response would not die away (system is unstable because of the factor eζ·ω·t). Rheologic behavior of the bar can be characterized by one parameter, i.e. dynamic time of retardation TKD=1/ω, like in a single-degree-of-freedom spring mass system. RDA model has the same phase angle as a simple single-degree-of-freedom spring mass system with damping in the steady state vibration and from that the damping factor is obtained. This paper provides description of the dynamic magnification factor and the transmissibility of several metallic materials using RDA similitude and could be concluded that an ideally effective antivibration mount material should satisfy at least two requirements: first, it should posses a relatively large damping factor; and second, it should possess a damping factor that either remains constant or decreases only slowly with frequency.


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