Free Oscillations of Euler-Bernoulli Beams on Nonlinear Winkler-Pasternak Foundation

In this paper the free oscillations of a simply supported Euler-Bernoulli beam resting on a nonlinear spring bed with linear and cubic stiffness are studied. The system is discretized by means of the classical Galerkin procedure and its nonlinear dynamic behaviour is analyzed using the Optimal Auxiliary Functions Method (OAFM). Frequency responses are presented in a closed form and their sensitivity with respect to the initial amplitudes are investigated. It is proved that OAFM is a reliable and straightforward approach to solve a set of coupled nonlinear differential equations.

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