Dynamic response spectra of fractionally damped viscoelastic beams subjected to moving load

Abstract

The dynamic response spectra of fractionally damped viscoelastic beams subjected to concentrated moving load are presented. This work quantitatively emphasizes the need for fractional-order damping model in the dynamics of viscoelastic structures, by demonstrating the effect of various orders of fractional derivative damping in beams subjected to concentrated moving loads. The fractional-order Kelvin–Voigt model describes the rheological properties of the viscoelastic material. The Riemann–Liouville fractional derivative of order 0<α ≤ 1 is applied. The complex natural frequencies of viscoelastic beams are studied with respect to α. The forced vibration response is investigated for a wide range of speeds of the moving load, encompassing all practical applications. The results obtained from the fractional-order damping model and the integer-order damping model are compared. With an increase in the order of the fractional derivative, the system damping of the system increases and the dynamic amplification factor (DAF) decreases, especially in the dynamic zone of the sweep parameter. Thus, an integer-order mechanical model over-predicts the damping and under-predicts the dynamic deflections and stresses. The fractional-order of derivative significantly influences the natural frequency, damping coefficient, and DAF. The results are verified with the literature.

Communicated by Jie Yang.

Keywords:

• Viscoelasticity
• fractional damping
• moving load
• amplification factor
• response spectra