Beating our chest is a sign of mourning and sadness on the tragedies of Ahlul Bayt(AS). It was practiced by early Muslims including Ayisha on her father's death (al-Tabaqaat al-Kubba by Ibn Sa'd, V.2, P.201), and pious believers on the tragedies of Ahlul Bayt (AS).
It is not self violence but expressing our feelings which helps us as well as confirm our love and attachment with the Prophet (SAWA) and his Progeny Ahlul Bayt (AS).
Wassalam.