DYNAMIC ANALYSIS OF NONLINEAR STRUCTURAL SYSTEMS BY MEANS OF FRACTIONAL CALCULUS

In this article the vibrational analysis of non-linear systems by means of fractional calculus is presented. This kind of non-linear problems appears in many areas of mechanical engineering, such as the contact in bearings, complex behavior materials, great displacements, vibrations in buildings, etc. The aim of this study is to find an alternative to methods like Runge-Kutta, which duplicate the number of equations to solve. The aim is, therefore, to apply traditional methods in structural mechanics that mantain the size of the system, like, for instance, the finite central difference method. For that it is necessary to linearize the system of equations. The proposed method transforms the original non-linear problem into fractional linear integro-differential equations, where the fractional operator represents a variable stiffness. Two typical application examples in mechanical engineering are presented: the elastic impact of two spheres (system of one degree of freedom) and the transient dynamic response of a building (system of multiple degrees of freedom) under the effect of a wind load. From the obtained results it can be concluded that the proposed method describes correctly the time response of the studied systems, reducing the computational effort.