Experimental, Numerical and Analytical Investigation of the Torsional Vibration Suppression of a Shaft with Multiple Optimal Undamped Absorbers

The aim of the present work is to study the suppressed torsional vibration of shafts, with a clamped boundary condition at either end, via single or multiple undamped absorbers. Structures with such features often suffer from failures (e.g. fatigue, wear) caused by excessive vibrations. The shaft considered is under the action of a harmonic point moment. A vibration design benchmark for torsional absorbers is presented. For both cases of the shaft with one and two absorbers, the variation of absorber parameters, including attaching position, moment of inertia and torsional stiffness, are investigated. The optimal values of the absorber control parameters are obtained. First, the governing equation for the torsional vibration of the shaft and its absorbers is derived in a dimensionless form. Next, the free and forced vibrations of the system are investigated and dimensionless natural frequencies are obtained. To absorb the identified natural frequencies, we compute the $${L}_{2}$$ norm of the angular displacement of the shaft at these frequencies and tune the parameters of the absorbers to minimize the norm. A detailed analytical solution framework for determining the torsional vibration response of a shaft equipped with torsional vibration absorbers is developed. Minimizing the established relations for the $${L}_{2}$$ norm of the shaft’s torsion is examined for a wide range of frequencies, as a criterion for determining its absorption frequency. Advantage of using two absorbers over a single absorber is highlighted. Validation of the analytical model is achieved by comparisons to both numerical and experimental results.