Andrei Zagvozdkin | Searcharxiv

arXiv2023

Hysteresis resulting from Lennard-Jones interactions

The fundamental mechanism of hysteresis in the quasistatic limit of multi-stable systems is associated with transitions of the system from one local minimum of the potential energy to another. In this scenario, as system parameters are (quasistatically) varied, the transition is prompted when a saddle-node bifurcation eliminates the minimum where the system resides in. The objective of the present work is to specify this generic mechanism for systems of interacting particles assuming a natural single-well (Lennard-Jones) interaction potential for each pair of particles. We show multi-stability and present details of hysteresis scenarios with the associated bifurcations and transitions in a case study of constrained four-degrees-of-freedom four particle systems on the plane.

cond-mat.mtrl-sci↗

arXiv2022

Dynamics of inertial pair coupled via frictional interface

Understanding the dynamics of two inertial bodies coupled via a friction interface is essential for a wide range of systems and motion control applications. Coupling terms within the dynamics of an inertial pair connected via a passive frictional contact are non-trivial and have long remained understudied in system communities. This problem is particularly challenging from a point of view of modeling the interaction forces and motion state variables. This paper deals with a generalized motion problem in systems with a free (of additional constraints) friction interface, assuming the classical Coulomb friction with discontinuity at the velocity zero crossing. We formulate the dynamics of motion as the closed-form ordinary differential equations containing the sign operator for mapping both, the Coulomb friction and the switching conditions, and discuss the validity of the model in the generalized force and motion coordinates. The system has one active degree of freedom (the driving body) and one passive degree of freedom (the driven body). We demonstrate the global convergence of trajectories for a free system with no external excitation forces. Then, an illustrative case study is presented for a harmonic oscillator with a frictionally coupled second mass that is not grounded or connected to a fixed frame. This simplified example illustrates a realization and main features of the proposed (general) modeling framework. Some future development and related challenges are discussed at the end of the paper.

eess.SY↗