Thanks to the development of deep learning, research on machine anomalous sound detection based on self-supervised learning has made remarkable achievements. However, there are differences in the acoustic characteristics of the test set and the training set under different operating conditions of the same machine (domain shifts). It is challenging for the existing detection methods to learn the domain shifts features stably with low computation overhead. To address these problems, we propose a domain shift-oriented machine anomalous sound detection model based on self-supervised learning (TranSelf-DyGCN) in this paper. Firstly, we design a time-frequency domain feature modeling network to capture global and local spatial and time-domain features, thus improving the stability of machine anomalous sound detection stability under domain shifts. Then, we adopt a Dynamic Graph Convolutional Network (DyGCN) to model the inter-dependence relationship between domain shifts features, enabling the model to perceive domain shifts features efficiently. Finally, we use a Domain Adaptive Network (DAN) to compensate for the performance decrease caused by domain shifts, making the model adapt to anomalous sound better in the self-supervised environment. The performance of the suggested model is validated on DCASE 2020 task 2 and DCASE 2022 task 2.