Wymuszone Drgania Skrętne Pręta z Materiału Lepkosprężystego

This paper concerns the forced twisting vibrations of a rod made of visco-elastic material. We have considered a rod having a constant, circular cross-section made of material without ageing. One end of the rod is immobilized, and a torque M(t) = M0 sinωt acts on the second end of the rod. Utilizing Boltzmann's principle of superposition, we obtain the equation of twisting vibrations. of the rod, Eq. (2.5) in the text. We present the general, exact method of solution of the problem.
We have performed detailed calculations for two simple rheological models -the Maxwell model and the Kelvin-Voigt model. A more accurate investigation only. Since the consecutive terms of the series involved in the amplitude of vibrations decrease: following I/(2n – 1)4, it is possible to confine the numerical calculations to a few of the first terms of the series. The contributions to the amplitude of vibration are considered separately, originating form the first two terms and the amplitude in the second approximation. In the drawings (2 to 5) included, is represented the amplitude of vibration of the free end of the rod depending on the dimensionless parameter, proportional to ω, for two different values of the parameter ß1, connected with the coefficient of viscosity.