Modal analysis of vibrations in liquid-filled piping systems

The vibration of liquid-filled piping systems is formulated using one-dimensional wave theory in both the liquid reaches and the pipe wall. Five families of waves and fourteen variables are considered and the effects of shear deformation and rotary inertia on the lateral vibration of the pipe reaches are included. A numerical model is described which includes both Poisson and junction coupling, thereby providing comprehensive interaction between the fluid reaches and the piping.; The transfer matrix method is used to study the motion of these systems. The motion is represented by an overall transfer matrix. This matrix is assembled by combining field transfer matrices representing the motion of single pipe reaches with point matrices describing specified boundary conditions.; A one-inch (25 mm) diameter variable length piping system with a U-type bend is used to obtain the experimental data. Various fluid and structural frequencies are excited by using a crank mechanism which vibrates the piping. Fluid pressure and pipe displacement responses for various forcing frequencies are obtained and compared with analytical results. Larger fluid pressure responses occur at higher harmonics than at the first fundamental frequency. Mode shapes for the liquid pressure and pipe motion are also presented. Good agreement of natural frequencies is found between predictions and observations.