The knowledge of how pipework respond to dynamic loads is important for the integrity and reliability of any hydrocarbon processing plant or module. Vibration of pipework can be machine-, flow- or acoustic-induced which means that the excitation frequencies of interest can vary from low frequencies (tens of Hz) to relatively high frequencies (1-2 kHz). For low-frequency excitations, simplified models can be used; however, these are sometimes not sufficient as the detailed displacement/stresses are sought to ensure the integrity of the system. In this case, finite element analysis (FEA) is often the technique of choice. However, for high-frequencies, FEA becomes computationally expensive and may not be cover the whole frequency of interest. To put things in perspective, a typical flowline will have hundreds of modes above 300 Hz; in this case, the number of degrees of freedom needed for the FEA rises exponentially and the analysis becomes prohibitive.
This paper presents a novel computationally efficient method for the analysis of the vibration of pipework. The method relies on the wave and finite element (WFE) method where the structural vibration of the pipework is represented in terms of the waves that travel in the pipe. A case study is presented where the reflection/transmission characteristics of a bend in a U-shaped pipework is investigated. The WFE formulation presents a number of other advantages compared to FEA: the models are obtained by just meshing a strip along the circumference of the pipe which means that the size of the model is very small; this immediately translates in shorter computation times. Thus, the WFE expands the limits of standard FEA and can be immediately used to predict the stress levels in pipework which is essential to assess the risk of vibration induced fatigue failure.