A method to determine structural patterns of mechanical systems with impacts

TL;DR

This paper introduces a new matrix-based classification method for vibro-impact mechanical systems, enabling systematic identification of all structural patterns in systems with any finite degrees of freedom.

Contribution

It presents a novel matrix representation and procedures for identifying and classifying structural patterns of vibro-impact systems with arbitrary degrees of freedom.

Findings

Developed a new matrix representation for impact systems

Created procedures for identifying equivalent and connected systems

Enabled comprehensive classification of structural patterns

Abstract

A structural classification method of vibro-impact systems with an arbitrary finite number of degrees of freedom based on the principles given by Blazejczyk-Okolewska et al. [Blazejczyk- Okolewska B., Czolczynski K., Kapitaniak T., Classification principles of types of mechanical systems with impacts - fundamental assumptions and rules, European Journal of Mechanics A/Solids, 2004, 23, pp. 517-537] has been proposed. We provide a characterization of equivalent mechanical systems with impacts expressed in terms of a new matrix representation, introduced to formulate the notation of the relations occurring in the system. The developed identification and elimination procedures of equivalent systems and an identification procedure of connected systems enable determination of a set of all structural patterns of vibro-impact systems with an arbitrary finite number of degrees of freedom.