Deep learning has been increasingly employed in data -driven structural health monitoring (SHM), forming a new paradigm of assessing structural conditions and identifying structural damage. Many structural damage classification methods rely on the assumption that the data of training and test (application) phases are closely distributed, thereby allowing trained models to generalize to the test data effectively. However, these approaches often face challenges in realworld scenarios as test data are unlabeled and their distributions can differ due to environmental and operational variabilities (EOVs). Additionally, the test data might include unknown damage classes not present in the labeled data. Both EOVs and unknown damage classes can decrease the performance of current classification methods. To address these challenges, we propose a deep domain adaptation framework for structural damage classification under varying environmental conditions, as well as taking unknown classes into account. The framework leverages an enhanced feature extraction module and proposes a domain alignment module to learn damagediscriminative , unknown-aware , and domain-invariant features, from vibration data. We validate the proposed framework on two real -world structures, a laboratorial wind turbine blade, and a lattice mast structure. Comparative analyses, contrasting our method with non-adapted and other domain adaptation methods, demonstrate the proposed framework's effectiveness across EOVs and the occurrence of unknown damage classes.