Relationship between the contact force strength and numerical inaccuracies in piecewise-smooth systems. (15th November 2021)

• Record Type: Journal Article
• Authors: Saunders, B.E.; Vasconcellos, R.; Kuether, R.J.; Abdelkefi, A.
• Is Part Of: International journal of mechanical sciences. Volume 210(2021)
• Publication Date: 2021-11-15
• Subjects: Freeplay nonlinearity -- event location -- numerical accuracy -- isolated resonances -- multistable solutions; Mechanical engineering -- Periodicals; Génie mécanique -- Périodiques; Mechanical engineering; Maschinenbau; Mechanik; Zeitschrift; Periodicals; 621.05
• DOI: 10.1016/j.ijmecsci.2021.106729
• Languages: English
• ISSNs: 0020-7403

Abstract

Highlights: Effects of the contact stiffness strength on the types of inaccuracies in freeplay-based systems. Event location method validated with experimental forced Duffing-freeplay oscillator. Method captures isolated resonances, chaos, and grazing contact. Comparing with/without event location shows basin of attraction boundaries are affected. Individual attractor solutions are relatively unaffected or slightly coarser. Abstract: This work studies the different types of behavior and inaccuracies that can occur when contact is not adequately accounted for in a dynamical system with freeplay, as the strength of the contact stiffness increases. The MATLAB® ode45 time integration solver, with the built-in Event Location capability, is first validated using past experimental data from a forced Duffing oscillator with freeplay. Next, numerical results utilizing event location are compared to results neglecting event location in order to highlight possible numerical errors and effects on multistable dynamical responses. Inaccuracies tend to occur in two different ways. First, neglecting event location can affect the boundaries between basins of attraction. Second, neglecting event location has little effect on the behaviors of the attractor solutions themselves besides merely resembling poorly converged solutions. Errors are less pronounced at the limits of soft or hard contact stiffness. This study shows the importance of accurately solving piecewise-smooth systems and the existing correlation between the strength of the contact force and possible numerical inaccuracies. Graphical Abstract: Image, graphical abstract