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Title: Parametric bifurcation of a viscoelastic column subject to axial harmonic force and time-delayed control
Author(s): Leung, Andrew Yee Tak 
Author(s): Yang, H. X.
Chen, J. Y.
Issue Date: 2014
Publisher: Elsevier
Journal: Computers & Structures 
Volume: 136
Start page: 47
End page: 55
We investigate the steady state response of a simply supported viscoelastic column subject to axial harmonic excitation. The viscoelastic material is modeled in fractional derivative Kelvin sense. The equation of motion is derived and discretized by the Galerkin approximation resulting in a generalized Mathieu–Duffing equation with time delay. Bifurcations in parametric excitation can be eliminated by appropriate feedback gain and time delay. The bifurcating behavior for various fractional orders and material ratios are also investigated. New criteria of stability determination are established. Based on the Runge–Kutta method, numerical results are obtained and compared with analytical solutions for verification.
DOI: 10.1016/j.compstruc.2014.01.015
CIHE Affiliated Publication: No
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