Brief note: viscoelastic modelling of cantilever vibration absorbers

AbstractInternal damping is considered in a cantilever beam supported on a single degree-of-freedom vibrating system. The internal damping mechanism is modelled by a Voigt viscoelastic coefficient in the stress-strain law. The governing equations reduce to a partial differential equation with time-dependent boundary conditions. The solution yields expressions for the amplitude ratio in terms of the tuning and frequency ratios, as well as the viscoelastic damping coefficient. These results are simulated numerically on the computer to obtain three different plots of the frequency response. The first plot has parametric values of the number of cantilevers. In the second plot, three parametric values of the internal damping coefficient are portrayed; the third plot shows the frequency response with various values of the natural frequency of the main system. These results show advantages in using cantilever beams with internal damping as dynamic vibration absorbers