Effective Modelling of Sticking Motions in Vibro-Impacting Continuous Systems

Abstract

In this work we propose a new methodology to simulate sticking motions occurring in vibro-impacting continuous systems. We have developed this method in the framework of the coefficient of restitution approach. During the sticking phase, the sticking constraints are imposed exactly using a Lagrange multiplier, which represents the reaction between the continuous system and the obstacle. The expression for the Lagrange multiplier is developed in closed form. The proposed method does not require the mode-shapes during the sticking phase, unlike the mode-switching method. The developed methodology is supported by illustrative numerical simulations.

Effect of Method Type on the Response of Continuum Vibro‐Impact

“…e key to this problem is the precise modeling and solution of the vibro-impact process. ere are three main modeling methods that have been reported in the past literature, which are based on force integration [4][5][6], mode transfer [7][8][9][10], and velocity restitution coefficient [11][12][13][14], respectively. Furthermore, according to whether or not they ignore the impact process time, the above methods can be divided into the following two categories:…”

“…Toulemonde and Gontier were the first to study this phenomenon systematically, based on the P-C method; the characteristics of the sticking motion of the single-degree-of-freedom and multidegree-of-freedom systems were investigated [19]. Separately, Vyasarayani et al used the CoR method to study the sticking motion in the vibro-impact of a beam and deduced the Lagrange multiplier when the system is in the sticking stage [14].…”