Identifying rumor sources in online social networks (OSNs) plays a crucial role in controlling the spread of rumors and mitigating their damage. However, the community structure of OSNs and timeliness of rumors increase the complexity of accurately characterizing rumor-spreading behavior, making it extremely challenging to identify the source of rumor in OSNs. Conventional studies on rumor source identification often overlook the community structure of OSNs and timeliness of rumors. This paper proposes a rumor sources identification framework that take these two aspects into consideration. First, we transfer the snapshots of a dynamic OSN into a community-structured dynamic OSN through 4 meticulously designed phases. Second, instead of considering a constant influence of rumors in traditional techniques, we introduce a time-varying dynamic propagation parameter to quantify the timeliness of rumor, and apply the propagation parameter to establish a microscopic rumor spreading model. This process addresses the issue of modeling the timeliness of rumor. Third, we adopt sensor-based observation techniques to collect the propagation information of rumor, and a hybrid sensor deployment strategy is designed to improve the efficiency of information collection. Fourth, we propose an algorithm for identifying single and multiple rumor sources in community-structured dynamic OSN, this algorithm initiates with the utilization of some criteria to analyze the gathered propagation information and estimate the suspicious communities that harbor the source of rumors. Subsequently, it applies maximum likelihood estimation method within each community to determine the ultimate source of the rumor. Experimental results on real-world and synthetic networks indicate that our method can accurately identify the real rumor sources. To the best of our knowledge, the proposed method is the first that can be used to identify rumor sources in community-structured dynamic OSNs.