Study on the design method of distorted model testing for cementing casing string systems based on the similarity of stiffness and mass

In the test design of large-scale scaled models (complete similarity models) of the cementing casing string systems (CCSS), the large length-diameter ratio of the casing string causes the wall thickness of model too thin to manufacturing. Therefore, this study proposes a test design method based on similarity in stiffness and mass for the unequal scale scaled models (distorted similarity models) of the CCSS. Firstly, a dynamic model of the CCSS is established and solved by the separation of variables method and modal superposition method. The accuracy of the dynamic model and the efficiency of the solution are verified by tests and finite element analysis respectively. Then, based on the dynamic model and its analytical solution, the equation analysis method is used to derive the similarity criteria for the complete similarity model of the system. Based on theoretical calculations, it is found that the predicted vibration characteristics and dynamic response results of the prototype system through the complete similarity model are highly accurate. To further solve the problem of difficulty in manufacturing complete similarity model tests with large scaling ratios, considering the similarity of the quality and stiffness of the CCSS, the similarity criteria for the distorted similarity model of the CCSS is derived. In order to achieve high accuracy in theoretical calculation and prediction, the length-diameter ratio of the model needs to be greater than 60. The correctness of predicting the prototype dynamic response through the distorted similarity criterion is verified through theoretical models and test, and a detailed process for designing the similarity model experiment of the CCSS is provided. Finally, robustness analysis, sensitivity analysis, and uncertainty analysis are conducted on the dynamic response and similarity criteria of the CCSS under different parameters. The analysis results indicate that the similarity criterion can accurately predict the vibration characteristics and response of the prototype under different parameter distortions. When the uncertainty interval of each parameter in the system is 10 %, the error of the natural frequency and response prediction results of the system is less than 0.6 %, which can be ignored. The impact of manufacturing accuracy in the actual model experiment design process can be ignored. This study provides a new approach for the experimental design of dynamic similarity models of large aspect ratio cementing casing systems.