Forced Vibration of Axially Accelerating three Parameter Beam Constituted by Fraction Alderivative Model

Abstract

Abstract The forced vibration characteristics of axially variable speed viscoelastic beams are studied. The material is described by the three parameter model of Poynting-Thompson beam. According to Newton's second law, the fractional derivative is introduced to deduce the governing equation of the beam. The approximate analytical solution and amplitude frequency equation are obtained by multi-scale method. The amplitude frequency equation is divided into real part and imaginary part by separating variables. According to the Routh-Hurwitz criterion, the Jacobi matrix and characteristic equation are established to determine the stable region and unstable region obtained under different parameters. Numerical examples show that the instability region shows a downward trend with the increase of the order of fractional derivative.