Three dimensional vibration analysis of liquid-filled piping systems

In the theoretical part of this work, the transfer matrix method (TMM) is employed to study the free vibration analysis of liquid-filled (air/water) piping systems. The existing governing equations which consist of a set of fourteen linear differential equations of first degree are considered. Fixed-fixed and fixed-free ends are studied with five different basic geometries of piping systems made of either copper or steel, such as single-span, L-bend, Z-bend, U-bend and 3-D bend. A few experiments are also completed to support the theoretical solutions. The effect of the elastic foundation on the natural frequencies is also studied. Finally, a parametric study is carried out to understand correctly the vibrational behavior of such systems. Present results are verified with the frequencies available in the literature.