On the passive control of vibrations with viscoelastic dynamic absorbers of ordinary and pendulum types

Dynamic vibration absorbers (DVA) provide a cheap and efficient means for vibration abatement in many complex systems, ranging from crankshafts of internal combustion engines, overhead transmission lines, machine casings, structural panels and large turbo machinery sets, to quote a few examples. One can provide a simple classification for them by considering the nature of the resilient material it contains as a form of “spring”: it may be viscous (CDVA), hysteretic (HDVA) or viscoelastic (VDVA). Viscous DVAs are the largely studied devices and one of their most remarkable applications is in mitigating crankshafts torsional vibrations and in very tall buildings. The most well known hysteretic DVA is the Stockbridge damper, largely applied in overhead electric power transmission lines. With modern use of fractional calculus, modelling viscoelastic materials became a routine work. The experimental identification of four fractional parameter models for viscoelastic material has become a standard technique amongst the authors of this work. Modelling viscoelastic materials by four fractional parameters has made advanced analysis of structures and systems where it is applied much more straightforward than it was before. This is true also for structures with VDVA and HDVA attached to it. In this paper it is shown that a hysteretic material model can be derived from a viscoelastic material model based on four fractional parameters. Generalized quantities of ordinary and pendulum type absorbers and for both viscoelastic and hysteretic materials are derived and their nature discussed. The performances of a system with absorbers of viscoelastic and hysteretic nature are compared. Input energy and dissipated energy by the absorbers of both natures and types are computed and compared, using the concept of generalized damping parameter of the absorbers. Conclusions are drawn from the comparisons. One of the ideas behind these computations is to check the validity of some international recommendations for the experimental assessment of Stockbridge dampers, which implicitly neglects the effect of the generalized mass parameter.