People's daily lives involve numerous periodic behaviors, such as eating and traveling. Local-life platforms cater to these recurring needs by providing essential services tied to daily routines. Therefore, users' periodic intentions are reflected in their interactions with the platforms. There are two main challenges in modeling users' periodic behaviors in the local-life service recommendation systems: 1) the diverse demands of users exhibit varying periodicities, which are difficult to distinguish as they are mixed in the behavior sequences; 2) the periodic behaviors of users are subject to dynamic changes due to factors such as holidays and promotional events. Existing methods struggle to distinguish the periodicities of diverse demands and overlook the importance of dynamically capturing changes in users' periodic behaviors. To this end, we employ a Frequency-Aware Multi-View Interest Modeling framework (FIM). Specifically, we propose a multi-view search strategy that decomposes users' demands from different perspectives to separate their various periodic intentions. This allows the model to comprehensively extract their periodic features than category-searched-only methods. Moreover, we propose a frequency-domain perception and evolution module. This module uses the Fourier Transform to convert users' temporal behaviors into the frequency domain, enabling the model to dynamically perceive their periodic features. Extensive offline experiments demonstrate that FIM achieves significant improvements on public and industrial datasets, showing its capability to effectively model users' periodic intentions. Furthermore, the model has been deployed on the Kuaishou local-life service platform. Through online A/B experiments, the transaction volume has been significantly improved.