A transfer matrix method-based closed-form solution of sensitivities of dynamic properties and FRF for multi-span pipes under complex boundary conditions

• Published in: Mechanical systems and signal processing 2023-09, Vol.198, p.110428, Article 110428
• Main Authors: Wang, Ze-Chao, Yan, Wang-Ji, Yuen, Ka-Veng
• Format: Article
• Language: English
• Subjects: Complex boundary conditions; Multi-span pipe; Sensitivity analysis; Structural model updating; Transfer matrix method
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2023.110428

•Sensitivity analysis of dynamics is studied for multi-span pipes under complex boundary conditions.•Closed-form solutions of sensitivities of dynamic properties and FRF are derived using TMM.•The difficulty in analytically solving characteristic determinant is addressed with algebraic method.•No truncation errors are involved in the analytical formula.•The parametric analysis lay a solid foundation for the design and structural health monitoring of pipes. The calculation of the first derivatives of dynamic properties and the frequency response functions with respect to design variables is a prerequisite for structural model updating and structural design. However, research about the sensitivity analysis of multi-span fluid-conveying pipes is still rarely performed. In this study, the closed-form formulae for the sensitivities are derived based on the transfer matrix method. Specifically, the difficulty in solving the sensitivities of the nonlinear eigenvalue problem is addressed from the characteristic determinant by invoking the implicit function theorem. One major advantage of the proposed method is that the closed-form formulas of sensitivities are given and no truncation errors are involved when compared with modal method and finite difference method. The method can explicitly deal with the analysis of the sensitivities of a pipe with arbitrary spans and accessories for complex boundary conditions. A three-span pipe is used to demonstrate the effectiveness and advantages of the method. The parametric eigenvalue sensitivity analysis provides useful design information and clamp looseness identification with structural model updating.