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A discrete model for nonlinear vibrations of a simply supported cracked beams resting on elastic foundations

Khnaijar A., Benamar R.

Diagnostyka

2017

Vol. 18, No. 3

39--46

The present paper introduces a discrete physical model to approach the problem of nonlinear vibrations of cracked beams resting on elastic foundations. It consists of a beam made of several small bars, evenly spaced, connected by spiral springs, presenting the beam bending stiffness. The crack is modeled by a spiral spring with a reduced stiffness and the Winkler soil stiffness is modeled using linear vertical springs. Concentrated masses, presenting the inertia of the beam, are located at the bar ends. The nonlinear effect, due to the axial forces in the bars resulting from the change in their length, is presented by longitudinal springs. This model has the advantage of simplifying parametric studies, because of its discrete nature, allowing any modification in the mass and the stiffness matrices, and in the nonlinearity tensor, to be made separately. After establishing the model, various practical applications are performed without the need of going through all the formulation again. Numerical linear and nonlinear results are given, corresponding to a cracked simply supported beam.