DAMPING DESCRIPTION INVOLVING FRACTIONAL OPERATORS

Structural damping is frequently approximated in the frequency domain by the constant hysteretic damping model. Transient vibrations of a member with constant hysteretic damping leads to a non-causal precursor response. The non-causal response can be avoided by introducing actual measured frequency dependent stiffness and damping behaviour of the material, or by introducing constitutive equations of differential operator type with classical derivatives (integer order) or generalised type (fractional order). This paper uses and generalises constitutive equations of viscoelastic behaviour of materials and members in the time and frequency domain. Weak frequency dependence of actual viscoelastic material can be fitted using only a few parameters by adopting the fractional derivative concept. The impulse response function of an oscillator with a fractional derivative damping model is integrated in the present paper with a new efficient technique using the inverse Fourier transform, this requires a unique definition of the constitutive equation in the frequency domain. The response is shown to fulfill causality requirements. Amplitude decay of the considered damping models are compared after selection of equivalent damping properties. © 1991.