High frequency vibration calculation methods for PFCPs

Abstract

The classical transfer matrix method (CTMM) is widely used in investigating the dynamic behavior of fluid-conveying pipes. When the fluid-conveying pipe is too long or the frequency is too high, the issue of unstable numerical solutions often occurs. In response to this, several improved transfer matrix methods have been developed to improve the numerical stability of the CTMM. Nevertheless, most of these methods are primarily suited for single fluid-conveying pipe systems. There is a scarcity of studies addressing the numerical stability issues and the associated improvement techniques in parallel fluid-conveying pipes (PFCPs). Therefore, this study first establishes a dynamic model of the PFCPs, and investigates the numerical stability challenges associated with applying the CTMM to solve such systems. Additionally, a sensitivity analysis is performed to evaluate how various parameters influence numerical stability. The results indicate that the PFCPs exhibit numerical instability issues in axial, lateral, and torsional vibrations. This instability arises because the elbow pipe induces coupling among vibrations in different directions. Additionally, each single pipe within the PFCPs also demonstrates numerical instability across all vibration modes due to structural coupling. Among various factors, the length of the pipe is identified as the most critical parameter affecting its numerical stability. The hybrid energy transfer matrix method (HETMM) and stiffness transfer matrix method (STMM) are efficient approaches for improving the numerical stability of the CTMM by reducing the characteristic length. However, when applied to PFCPs, these methods result in singular and ill-conditioned matrices, thereby preventing the successful solution of such systems. Therefore, this study develops the improved hybrid energy transfer matrix method (IHETMM) and the improved stiffness transfer matrix method (ISTMM) by addressing the singular and ill-conditioned issues of matrices that arise during their solution processes. Finally, the validity of the two improved methods is confirmed through comparisons with five existing examples, while their stability and efficiency are demonstrated by contrasting them with currently improved transfer matrix methods. This study provides innovative approaches for the high-frequency numerical solution of PFCPs, thereby improving the numerical stability of CTMM in solving the dynamic response of such systems.