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

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.