In the analysis of liquid-filled piping systems there are Poisson-coupled axial stress waves in the pipe and liquid column, which are caused by the dilation of the pipe. In some conditions the influence of viscous friction that is usually frequency-dependent should not be omitted, which in fact is another kind of coupled form. It directly influences the amplitude of vibration of piping systems to some degree. The larger the viscosity of the liquid is, the greater the influence will be. Budny (1991) included the viscous friction influence in time domain analysis of fluid-structure interaction, but did not give frequency domain analysis. Lesmez (1990) gave the model analysis liquid-filled piping systems without considering friction. If the friction is not included in frequency domain analysis, the vibration amplitude will be greater than that when friction is included, especially at harmony points, cause large errors in the simulation of fluid pipe network analysis, although it may have little influence on the frequency of harmony points. The present paper will give detail solutions to the transfer matrix that represents the motion of single pipe section, which is the basis of complex fluid-structure interaction analysis. Combined with point matrices that describe specified boundary conditions, overall transfer matrix for a piping system can be assembled. Corresponding state vectors can then be evaluated to predict the piping and liquid motion. At last, a twice-coordinate transformation method is adopted in joint coupling. Consequently, the vibration analysis of spatial liquid-filled piping systems can be carried out. It is proved to be succinct, valid and versatile. This method can be extended to the simulation of the curved spatial pipeline systems.

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