This study deals with finite-time consensus problems of second-order multi-agent systems with intrinsicnonlinear dynamics and external bounded disturbances. First, instead of the time-triggered control algorithm, theevent-triggered control algorithm is developed by using integral sliding mode control strategy. Then, a triggeringfunction is explicitly constructed to generate event sequences, and the triggering function is fully continuous communicationfree. Rigorous proof is given by using Lyapunov stability theory and finite-time stability theory. Severalconditions are derived to guarantee the finite-time consensus and exclude Zeno behavior. Finally, a simulation ofsingle-link robotic arms is given to verify the effectiveness of the results.