A method is presented to compute the non-stationary response of single-degree-of-freedom structural systemswith fractional damping. Based on an appropriate change of variable and a discretization of the fractional derivative operator,the equation of motion is reverted to a set of coupled linear equations involving additional half oscillators, the number of whichdepends on the discretization of the fractional derivative operator. In this context, it is shown that such a set of oscillators can begiven a proper fractal representation, with a Mandelbrot dimension depending on the fractional derivative order a. It is then seenthat the response second-order statistics of the derived set of coupled linear equations can be built, in a closed form, forstochastic inputs of relevant interest in engineering practice. For this a preliminary eigenvector expansion shall be pursued. Themethod applies for fractional damping of arbitrary order a (0£ a £1). Results are compared to Monte Carlo simulation dataobtained based on a standard discretization of the Caputo’s fractional derivative.
|Numero di pagine||7|
|Stato di pubblicazione||Published - 2011|
All Science Journal Classification (ASJC) codes
- Hardware and Architecture
- Computer Networks and Communications
- Control and Systems Engineering
- Electrical and Electronic Engineering