On The Dynamic Analysis of Non-Uniform Beams With Non-Linear Winkler Foundation

Abstract

The problem being investigated in this paper is that of the dynamic response of a non-uniform beam subjected to uniformly distributed moving load resting on a horizontal plane. When the beam is loaded in the direction parallel to the horizontal plane, frictional forces resulting from the displacement of the beam under load will act against the direction of the applied load. Therefore, the frictional resistance caused by two surfaces sliding against each other obeys the logarithmic rule which when considered together with the behaviour of the beam produces a non-linear response to the applied load. In the same way, the elastic properties of the beam, the flexural rigidity, and the mass density per unit length, and the elastic modulus parameter are expressed as functions of the spatial variable x. However, the main objectives of this study is to investigate the effect of (i) non-linear constant parameter (ii) velocity of the moving load (iii) load’s length, and (iv) the span length of the beam on the dynamic response of beams on non-linear Winkler foundation.

Journal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 175 – 182