In this paper, a model reduction approach is employed to develop a reduced-order model of a trapezoidal corrugated plate structure for vibration analysis and structural optimization. A finite element dynamic model of the corrugated plate is first established using relative degree of freedom shell elements combined with Hamilton's principle. The model is then reduced using the Craig-Bampton (C-B) method. Furthermore, an efficient optimization framework for the corrugated plate structure is designed by integrating the C-B method with a genetic algorithm. The accuracy of the reduced-order model based on the C-B method is validated through a comparative analysis with the traditional finite element method. Numerical examples demonstrate that, although computational accuracy is slightly sacrificed, the reduced model significantly decreases the model size, with degrees of freedom reduced by over 95% and computational time shortened by more than 99%, resulting in a substantial improvement in computational efficiency. Additionally, the effectiveness of the genetic algorithm based on the C-B method is verified through two typical optimization examples, showcasing the notable advantages of model reduction in the dynamic analysis and structural optimization of corrugated plates.