Stability and orthogonality of fluid-structure interaction transfer matrix for liquid-filled pipeline systems

The study of the vibration characteristics of the liquid-filled pipeline has important academic significance and practical value for analyzing the dynamic behavior of the pipeline system, ensuring its stability and improving its reliability. The fluid-structure interaction transfer matrix method (FSITMM) is regarded as an effective method for the study of these vibration characteristics. Nonetheless, there are relatively few studies concerning the theoretical basis, especially stability and orthogonality, of the FSITMM for liquid-filled piping systems. The existing studies cannot adequately address computational failure issues in models based on the FSITMM, cannot determine whether the results are credible, and even more, cannot predict whether the new models will be computationally successful. The weighted orthogonality of the eigenvectors is a necessary condition for the modal synthesis method to determine the transient (or time-domain) response of the pipeline, and the stability is crucial as it guarantees the accuracy of the solution results. In this paper, the weighted orthogonality of the modes of the FSITMM for liquid-filled piping systems is validated, the stability of this transfer matrix is examined, and enhanced by the reduced transfer matrix method. Numerical simulation results demonstrate the ability of stability validation to predict the success of computational results, while weighted orthogonality validation can determine the accuracy of computational results. The results obtained from the fluid-structure interaction model using the approach of this paper are more accurate.