Parametric Instability of Viscoelastic Nonlinear (Elastica) Columns
The dynamic stability analysis of a uniform, homogeneous, simply supported column, subjected to a periodic axial force, is presented. The viscoelastic behaviour is given in terms of the Boltzmann superposition principle. The equation of motion, derived within the elastica and including variations in the column's length, is in the form of a nonlinear integro-differential equation. The stability analysis of this equation is carried out within the Lyapunov exponents concept, which is also used, together with the Fourier power spectrum, in order to examine the possibility of a chaotic situation.
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