Dynamic responses of undamped oscillator subjected to underwater shock wave

The dynamic response of underwater structures subjected to shock waves is of great interest to the defense and oil industries. This work analyses the fluid-structure interaction (FSI) effects during dynamic response of an undamped oscillator consisting of a mass block and a spring when it exposed to underwater blast loading and develops a theoretical model for predicting the motion history of mass block. The spring-loaded valve is selected as a typical undamped oscillator structure and subjected to explosion loading in a water tank. The displacement histories of the valve spool supported by various springs at different proportional distances are measured, and the conversion process between work done by shock wave and the kinetic energy of the valve spool and potential energy stored in the spring is analyzed. A one-dimensional unsteady flow model is developed based on the basic relationship of shock wave and the Tait equation of state for water, which has better universality due to its consideration of the compressibility of water. Using this theoretical model, the influence of the characteristic parameters of the shock wave and the structural parameters of the undamped oscillator on the fluid-solid interface pressure, energy conversion, and the motion response of the mass block are analyzed. The study found that the work done by the shock wave on the undamped oscillator is mainly converted into the kinetic energy of the mass block; this kinetic energy is then converted into the elastic potential energy and dissipated energy. The conversion rate of shock wave energy is mainly influenced by the dimensionless FSI coefficient and is independent of the specific strength of the undamped oscillator. Based on the relationship between energy conversion rate and FSI coefficient, an analytical solution for the displacement of the mass block is derived, along with a criterion to determine whether the mass block can reach the constraint boundary. The research results provide a reference for the motion response analysis of various structures subjected to underwater shock wave loadings and provide theoretical guidance for the design of spring-loaded pressure relief valves.