Fractional dissipation generated by hidden wave-fields

Abstract

This paper considers the damping induced on a single degree-of-freedom system when it is coupled at one end of a waveguide in which waves are radiated producing an energy loss in the oscillator motion that appears as a damping effect. In general, the whole system is described by the equation of the motion of the harmonic oscillator coupled with the wave equation of the propagation field. Hiding the variable that describes the wave motion and expressing it in terms of the oscillator vibration, a new equation for the oscillator is determined. In general, a nonconventional damping effect is born from the coupling terms. This paper examines cases in which the induced damping effect is of fractional-derivative type. This point of view produces physical examples of the way that simple mechanical structural systems, familiar to engineers, can exhibit fractional damping, a concept that does not always have a clear physical interpretation.