On the dynamics of Rayleigh beams resting on fractional-order viscoelastic Pasternak foundations subjected to moving loads

The standard averaging method is used to provide an analytical explanation on the effects of spacing loads, load velocity, order of the fractional viscoelastic property of shear layer material on the amplitude of the beam. The geometric nonlinearity is taken into account in the model. The analysis shows that, when the moving loads are uniformly distributed upon all the length of the structure, it vibrates the least possible. Moreover, as the order of the derivative increases, the resonant amplitude of the beam vibration decreases. In other hand, by means of Melnikov technique, a necessary condition for onset of horseshoes chaos resulting from heteroclinic bifurcation is derived analytically. We point out the critical weight of moving loads and order of the fractional derivative above which the system becomes unstable. (C) 2016 Elsevier Ltd. All rights reserved.