Transient Resonance Oscillations of a System with Fractional Derivative Damping of Order ½

The solution of the equation of motion of a system with one degree of freedom and the fractional derivative damping of order 1/2 in the case of transition through resonance with a constant acceleration is presented in the paper. An integral expression of Duhamel type is used to obtain the system response. The method proposed by Miller and Ross [Miller and Ross, 1993] is used to find Green’s function. The solution can be used in analysis for more complex systems such rods or beams. Illustrative examples of transient responses for the considered system with the fractional and first order derivative damping model are presented.