This article studies a periodic event-triggered distributed optimization algorithm for the optimal resource allocation of multi-agent systems under limited communication bandwidth. Based on the continuous-time distributed weighted gradient algorithm, a new Lyapunov function is proposed to synthesize an event-triggered communication mechanism. In this mechanism, each agent only needs to sample its own state information and evaluate the event-triggered condition at fixed intervals to determine whether communication is required. The stability analysis shows that the distributed optimization algorithm converges to the optimal solution at an exponential rate. The periodic event-triggered mechanism not only naturally eliminates Zeno behavior but also does not require real-time detection triggers. Finally, numerical simulations verify the effectiveness of the proposed distributed event-triggered optimization algorithm.