Parametric bifurcation of a viscoelastic column subject to axial harmonic force and time-delayed control.

Highlights: [•] We study a viscoelastic column subject to parametric excitation whose damping is governed by fractional derivatives. [•] We find the multiple bifurcation solutions, jump phenomenon and saddle-node analytically. [•] Nonlinear fractional derivative and time delay are investigated. [•] We find that the fractional order, time delay and material modulus ratio can increase the stability. [•] New criteria of stability determination for fractional order derivatives are established. [Copyright &y& Elsevier]