This paper considers the decentralised event-triggered consensus problem for multi-agent systems with Lagrangian dynamics under undirected graphs. First, a distributed, leaderless, and event-triggered consensus control algorithm is presented based on the definition of generalised positions and velocities for all agents. There is only one triggering function for both the generalised positions and velocities and no Zeno behaviour exhibited under the proposed consensus strategy. Second, an adaptive event-triggered consensus control algorithm is proposed for such multi-agent systems with unknown constant parameters. Third, based on sliding-mode method, an event-triggered consensus control algorithm is considered for the case with external disturbance. Finally, simulation results are given to illustrate the theoretical results.