VIBRATION CHARACTERISTICS OF AXIALLY MOVING TIMOSHENKO BEAM UNDER VISCOELASTIC DAMPING

Viscoelastic damping has always been one of the research hotspots of axial motion system. The influence of viscoelastic damping has not been considered in most previous researches on axial motion systems. In the present paper, the vibration characteristics of the axially moving Timoshenko beam with viscoelastic damping are studied. The dynamic equations of Timoshenko beams with axial viscoelastic motion and the corresponding boundary conditions of simply supported beams are obtained using the generalized Hamilton principle. The method of direct multiple scales is used to show the corresponding relationship between axial speed and parameters. The approximate analytical solutions of the first two natural frequency and attenuation coefficient are obtained. The differential quadrature method is applied to analyze the variation of the first two natural frequencies and attenuation coefficients with the axial speed under the presence or absence of viscoelasticity. The approximate numerical solutions of the first two natural frequencies and attenuation coefficients under viscoelastic action are given and the validity of approximate analytic solution is verified. It is shown that the natural frequency of the beam decreases gradually with the increasing axial speed. The natural frequency and attenuation coefficient of the beam decrease with the increasing viscoelastic coefficient. The attenuation coefficient is proportional to the viscoelastic coefficient. The viscoelastic coefficient has little effect on the first order attenuation coefficient and natural frequency. But it has a greater influence on the second-order attenuation coefficient and natural frequency.