A developed non-smooth coordinate transformation for general bilateral vibro-impact systems

Area of Science:

• Mechanical Engineering
• Nonlinear Dynamics
• Vibrational Analysis

Background:

• Vibro-impact systems present significant research challenges due to discontinuous dynamics.
• Existing methods like Zhuravlev and Ivanov transformations offer partial solutions but have limitations.

Purpose of the Study:

• To propose a novel, direct, and universal coordinate transformation for general bilateral rigid vibro-impact systems.
• To extend the applicability of impact-free analysis to systems with asymmetrical barrier positions and varying restitution coefficients.
• To demonstrate the method's utility for unilateral vibro-impact systems.

Main Methods:

• The proposed transformation is inspired by the Ivanov transformation technique.
• It ensures trajectory continuity in an auxiliary phase space, effectively bypassing impact terms.
• The methodology is validated through case studies on various vibro-impact system configurations.

Main Results:

• A direct and universal transformation applicable to general bilateral rigid vibro-impact systems has been successfully developed.
• The transformation effectively handles systems with asymmetrical barrier configurations and inconsistent restitution coefficients.
• The method's applicability was confirmed for unilateral vibro-impact systems.

Conclusions:

• The new coordinate transformation provides a more accessible and versatile tool for analyzing vibro-impact systems.
• This approach simplifies the study of complex dynamics by removing impact-related difficulties.
• The proposed methodology enhances the understanding and analysis of both bilateral and unilateral vibro-impact phenomena.