The stability problem associated with an Euler-Bernoulli beam made of an arbitrary linear viscoelastic material is formulated. The three parameter solid and the Kelvin-Voigt models are analyzed in the presence of constant as well as periodic loads. The application of a finite time stability concept is shown for the constant loading case when the traditional stability criterion fails to make sense. For the case of a periodic loading, the stability diagrams are obtained through an application of Floquet theory. It is found that the addition of periodic loads may significantly alter the stability behavior of a column which is originally subjected to a constant load only.

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