Vibration analysis of liquid-filled pipelines with elastic constraints

In this paper, a transfer matrix method (TMM) in frequency domain considering fluid–structure interaction of liquid-filled pipelines with elastic constraints is proposed. The time-domain equations considering fluid–structure interaction, are transformed into frequency domain by Laplace transformation, and then twelve fourth-order ordinary differential equations and two second-order ordinary differential equations are deduced from the frequency-domain equations. The results of the fourteen frequency-domain equations are assembled into a transfer matrix, which represents the motion of a single pipe section. Combined with point matrices that describe specified boundary conditions, an overall transfer matrix for liquid-filled pipeline system can be assembled. Using the method, all the pipeline with no and rigid constraints can be easily calculated by simply setting the stiffness of the restraining springs from zero to a large number. Taking into account the longitudinal vibration, transverse vibration and torsional vibration, the proposed method can be used to analyze the pipelines with bends. Several numerical examples with different constraints are presented here to illustrate the application of the proposed method. The results are validated by measured and simulation data. Through the numerical examples, it is shown that the proposed method is efficient.