Mathematical formulation of a dynamical system with dry friction subjected to external forces

PHYSICA D-NONLINEAR PHENOMENA

卷:421

Article

Bensoussan, A.^1,2  Brouste, A.³  Cartiaux, F. B.⁴  Mathey, C.⁵  Mertz, L.⁶ 

[1] Univ Texas Dallas, Jindal Sch Management, Richardson, TX 75083 USA

[2] Hong Kong City Univ, Sch Data Sci, Hong Kong, Peoples R China

[3] Le Mans Univ, Lab Manceau Math, Le Mans, France

[4] OSMOS Grp, Paris, France

[5] City Univ Hong Kong, Dept Math, Kowloon Tong, Hong Kong, Peoples R China

[6] NYU Shanghai, ECNU NYU, Inst Math Sci, Shanghai, Peoples R China

关键词: Dry friction;    Extended variational inequality;    Model calibration;   

DOI  :  10.1016/j.physd.2021.132859

来源: Elsevier

【 摘 要 】

We consider the response of a one-dimensional system with friction. Shaw (1986) introduced the set up of different coefficients for the static and dynamic phases (also called stick and slip phases). He constructs a step by step solution, corresponding to an harmonic forcing. In this paper, we show that the theory of variational inequalities (V.I.) provides an elegant and synthetic approach to obtain the existence and uniqueness of the solution, avoiding the step by step construction. We then apply the theory to a real structure with real data and show that the model qualitatively agrees with the real data. In our case, the forcing motion comes from dilatation, due to temperature. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free