DYNA JOURNAL ENGINEERING

Key words:

Dinámica estructural, rigidez no lineal, cálculo fraccionario, respuesta transitoria, métodos numéricos, Structural dynamics, nonlinear stiffness, fractional calculus, transient response, numerical methods.

Article type:

ARTICULO DE INVESTIGACION / RESEARCH ARTICLE

Section:

RESEARCH ARTICLES

A dynamical analysis of nonlinear structural systems by means of fractional calculus is presented. The reason for this study is to find an alternative to methods like Runge-Kutta which duplicate the number of equations to solve. The aim is, then, to linearize the system of equations and apply traditional methods in structural mechanics keeping the size of the system, like the finite central difference method. The proposed methodology transforms the original nonlinear problem into a fractional integro-differential equation, in which the fractional operator represents a variable stiffness. Two typical cases of application 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 multiples degrees of freedom). It is concluded from the obtained results that the proposed method describes correctly the response of the studied systems, reducing the computational cost.