Eventos Anais de eventos
DINAME 2023
XIX International Symposium on Dynamic Problems of Mechanics
Stick-slip oscillator: a stochastic approach for the run-time
Submission Author:
Mariana Gomes D. dos Santos , RJ
Co-Authors:
Mariana Gomes D. dos Santos, Hector Eduardo Goicoechea Manuel, Roberta Lima, Rubens Sampaio
Presenter: Mariana Gomes D. dos Santos
doi://10.26678/ABCM.DINAME2023.DIN2023-0021
Abstract
In this article, the run-times required to simulate an oscillator with uncertain dry-friction forces are studied from a stochastic perspective. The oscillator can exhibit stick-slip phenomena due to the discontinuos transition between the static and the dynamic friction. The hypothesis that the magnitude of the dry friction force and the duration of the stick phases may have a direct influence on the run-times is explored, as small time-steps are often required to capture the transition between phases when numerical integration is used. The stochastic problem is solved with the Monte Carlo method in combination with two different approximation strategies: a Runge-Kutta numerical integration and an analytical approximation based on the Multiple Scales method. In both cases, the run-time is treated as a random variable. Its dependency on parameters such as the dynamic friction coefficient, and statistics like the mean stick-duration or the number of sticks, is studied. The results, with 50000 realizations, show that the run-times with the analytical approach is, in mean, $3.68$ times faster than the numerical one, and it is also less sensitive to variations, considering that the standard deviation is $2.9$ times smaller than that obtained with the numerical scheme. The improvement observed in the run-times with the analytical method can be a determining factor for the feasibility of a stochastic study, given that the Monte Carlo approach requires a large number of realizations, which is time-costly.
Keywords
Analytical approximation, stick-slip phenomenon, Monte Carlo method, Computation cost
