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

Discontinuity and non-smoothness of system displacement and velocity caused by mechanical impact make the related research on dynamics of vibro-impact systems very difficult and complex. For the sake of bypassing the problems resulting from impact to some extent, Zhuravlev and Ivanov coordinate transformations were proposed, which can effectively convert the vibro-impact system to one without impact terms. In this paper, a more direct and universal transformation for general bilateral rigid vibro-impact systems is proposed. It is inspired by the main technique of Ivanov transformation, which makes the trajectories remain continuous in an auxiliary phase space. It can be directly applied to common vibro-impact systems, whether the positions of barriers are symmetrical or the restitution coefficients of barriers on both sides are consistent. In particular, this method can also be applied to the unilateral vibro-impact system. Validity of the proposed methodology is examined by means of case studies.