A generalized damped Beck’s column under non conservative autonomous and non autonomous actions governed by nonlinear partial integro-differential equations of motion is considered. The problem of deriving a discrete model for this nonself-adjoint system as well as criteria for a proper choice of the trial functions are discussed. Through a Galerkin approach, a discrete model capable of representing both critical and post-critical scenario is derived. Critical scenarios are shown and a good agreement between continuos and discrete approach is observed. The Multiple Scales Method is used in order to obtain the bifurcation equations in the neighborhood of a Hopf bifurcation point in primary parametric resonance.
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