Closed-Form Solutions for Forced Vibration of Multi-Span Fluid-Conveying Pipe System based on Green’s Functions

Multi-span fluid-conveying pipe systems are common models in the field of dynamics. This paper presents a novel systematic analytical approach for the dynamic analysis of such systems. The core innovation lies in recasting the multi-span system as an equivalent single-span one subjected to the support forces, thereby transforming a complex multi-support problem into a more tractable single-span dynamic problem with multiple external forces. Based on this concept, the closed-form solutions of forced vibration of the multi-span pipe system with grounded spring-dampers are obtained. The Green’s function method based on the Laplace transform is used to obtain the steady-state solutions of this system. The Green’s functions of the single-span pipe system are obtained by the traditional Laplace transform technique, while the Green’s function of the multi-span system is expressed by the Green’s function of the single-span system by means of the superposition principle. In the numerical discussion section, the reliability of the method proposed in this paper is verified, and the influence of support position, stiffness, etc. on the vibration response and frequency characteristics of the system is studied using the present method. The method is characterized by its clarity, programming convenience, and offers a fresh perspective for the dynamic research of multi-span fluid-conveying pipe systems.