TIME RESPONSE OF A POLYMER BEAM MODELED W ITH A FRACTIONAL VOIGT-KELVIN DAMPING

This paper shows how the fractional Voigt-Kelvin damping model can be used to simulate efficiently the behaviour in the time domain of a vib rating polymer beam. The fractional Voigt-Kelvin damping model is Hook e's law plus a fractional derivative of the strain, the fractional der ivative being a derivative of order alpha where alpha is between 0 and 1. We first include the fractional stress-strain damping model in the dynamics equations. An original numerical algorithm solving non-linea r ordinary differential equations including fractional derivatives is then outlined. With this algorithm, the behaviour of a vibrating beam of polymethylmethacrylate is simulated and compared to experimental re sults.