Parametric analysis of the statistical model of the stick-slip process

• Published in: Journal of sound and vibration Vol. 397; pp. 141 - 151
• Main Authors: Lima, Roberta, Sampaio, Rubens
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 09.06.2017; Elsevier Science Ltd
• Subjects: Coulomb friction; Dry-friction oscillator; Friction; Histograms; Non-smooth system; Parametric analysis; Parametric statistics; Poisson density functions; Probabilistic models; Random variables; Samples; Slip; Statistical analysis; Statistical methods; Statistical model; Statistical models; Statistics; Stick duration; Stick-slip; Stochastic process; Studies; Stick-slip; Parametric analysis; Statistical model; Non-smooth system; Stochastic process; Stick duration; Dry-friction oscillator
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2017.02.046

In this paper it is performed a parametric analysis of the statistical model of the response of a dry-friction oscillator. The oscillator is a spring-mass system which moves over a base with a rough surface. Due to this roughness, the mass is subject to a dry-frictional force modeled as a Coulomb friction. The system is stochastically excited by an imposed bang-bang base motion. The base velocity is modeled by a Poisson process for which a probabilistic model is fully specified. The excitation induces in the system stochastic stick-slip oscillations. The system response is composed by a random sequence alternating stick and slip-modes. With realizations of the system, a statistical model is constructed for this sequence. In this statistical model, the variables of interest of the sequence are modeled as random variables, as for example, the number of time intervals in which stick or slip occur, the instants at which they begin, and their duration. Samples of the system response are computed by integration of the dynamic equation of the system using independent samples of the base motion. Statistics and histograms of the random variables which characterize the stick-slip process are estimated for the generated samples. The objective of the paper is to analyze how these estimated statistics and histograms vary with the system parameters, i.e., to make a parametric analysis of the statistical model of the stick-slip process.