Nonlinear “Beam Inside Beam” Model Analysis by Using a Hybrid Semi-analytical Wavelet Based Method

Abstract

The previously developed model “beam inside beam” used for rail head vibrations analysis is extended by assumptions regarding viscoelastic nonlinear properties of the system. The coupled system of dynamic differential equations describes the beam-foundation structure subjected to distributed forces travelling along a beam. The upper beam, although arbitrarily distinguished, is not separated from the whole beam. This layer is considered as a vibration generator for the whole beam longitudinal axis. An assumption of nonlinear foundation stiffness is introduced as an important extension compared to existing solutions. This nonlinear system is solved by using a hybrid method based on the Adomian’s decomposition combined with a wavelet based approximation. Although description of the problem was already presented before, a new solution along with computational examples are important contribution to the field and the main novelty of the paper. The theoretical parameters used in the analysis are taken from the literature and although being close to real structures they should be validated by experimental measurements. The aim of this parametrical study is to compare the new “beam inside beam” model with classical system of double-beam resting on nonlinear foundation. This work is left however for future study.