A waveguide approach to the vibrational power flow in pipes with bends

The prediction of the flow of vibrational power in pipes is essential to evaluate the integrity and reliability of such structures, especially in petrochemical applications where mechanical failure due to high cyclic stresses can be catastrophic. In the low frequency range, standard finite element (FE) analysis can be used to analyse the vibrational behaviour based on a mode-by-mode approach. In the high frequency range, the energy is dispersed over the modes resulting in typically lower stresses. The mid-frequency range, however, is troublesome as there are many modes, each with its own characteristics, which prevents a mode-by-mode analysis. In this paper, a computationally efficient approach for predicting the flow of vibrational power in pipes with bends is presented. The approach is based on the wave and finite element (WFE) method. In principle, the WFE method relies on post-processing an FE model of a small segment of a homogeneous waveguide. The model can be obtained using any commercial or in-house FE package which allows the exploitation of existing meshing capabilities; for a pipe, only a small segment along its length should be modelled in FE. The wave propagation is then studied along the pipe's axis, yielding the wave characteristics of the pipe. Numerical results are obtained at negligible costs compared to full FE analysis. The approach is demonstrated by examining the power reflection and transmission ratios in a U-shaped pipe.