A Procedure for Calculating an Approximate Analytical Response in a Large Class of Mechanical Systems

Abstract:- Dynamical response in closed form is always a major goal when one wants to analyze the behaviour of a dynamical system. Nowadays, as is well known, we are able to calculate analytical response of mechanical systems only in a limited number of classes. So it is highly relevant to develop powerful methodologies which can help us in the dynamic analysis or in the non-linear identification processes of those systems. In this paper we present a direct and elegant procedure for calculating an approximate response of a large class of evolutionary equations which are of primary importance by the viewpoint of physics and engineering people. For instance this method could be used for identification of damping parameter of rotors, friction parameters in sliding process, and so on. The procedure consists of four steps: a Taylor transform, the use of a Lie operator followed by a linearization and finally the application of the corresponding Taylor’s inverse transform. A peculiarity of this method is that the Lie operator can be directly built by the Taylor transformation of the assigned evolutionary equation. The most important characteristic of this method is that it allows to calculate the response including, in explicit form, the whole parameters system. Consequently, this feature allows one to use very simple algorithms, as the Least Square Method for example, in order to develop quick non-linear identification processes