A new method of describing for vibration damping of a beam built-in at one end

We propose a new method of describing for vibration damping of a beam built-in at one end. The method takes into account dynamic hysteresis, which determines the dissipation of mechanical energy due to viscoelasticity. As a mathematical tool, we use fractional integro-differentiation. Experimental studies of rapidly damped vibrations of a foam polypropylene beam have been carried out. It is shown that the theoretical model successfully describes the experimental results.