Parametric bifurcation of a viscoelastic column subject to axial harmonic force and time-delayed control
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.
parametric bifurcation viscoelastic column time delay fractional mathieuduffing oscillator