Dynamic response analysis of a typical time-varying mass system: A moving-interface pipe model, the WKB-recursive solution and experimental validation

This research aims to seek a suitable way for analyzing the time-varying characteristics of some engineering phenomena such as the fuel consumption of flying rockets, the movement process of control rods used to regulate the reaction rate in nuclear reactors, etc. To address this problem, a simulated procedure containing modeling and response solving is proposed. A common variable cross-section pipeline with time-varying mass is designed as a practical time-varying system. A simplified segmented beam model with a moving interface is proposed to simulate the pipe's time-varying behavior. Then the Wentzel-Kramers-Brillouin (WKB)-recursive method is proposed to solve this time-varying problem. A two-segmented beam example is used to verify its computability. The computational efficiency is greatly improved in comparison with the conventional numerical integration methods. To validate this proposed procedure, numerical simulation is carried out and an experiment is specially designed and implemented. In the experiment, many cases of different rates of mass variation and excitation forces are carried out. Overall, the numerical dynamic responses match well with the experimental ones, which indicates that the proposed procedure is suitable for analyzing the system's time-varying characteristics.