Theoretical model of equipment-pipe-shell coupled system based on rayleigh-ritz method

Mechanical equipment is usually connected with pipes, e.g., pipe connected to diesel engine as fuel intake. In most cases, the mechanical vibration of equipment propagates along the pipe and generates vibration at the other end of the pipe. Elastic wave propagation in pipe, i.e., thin-walled shell, was studied since 1950s and different models were proposed, e.g., Kennard-Epstein shell theory. In the present work, a theoretical model of an equipment vibration propagates through a liquid filled pipe to an elastics shell was established based on Rayleigh-Ritz method. The coupling between the different components in the model was realized by the virtual spring method, while the coupling between the pipe wall and acoustic field in the fluid was realized by the boundary continuity condition. By solving the energy terms of each component in the model, the Lagrangian function of the system can be expressed, and then the dynamic equations of the system are derived. The theoretical model was validated by comparing the result with finite element simulation. Finally, a multi-layer pipe model was proposed based on the abovementioned method.