Spring-loaded valves are widely used to protect sealed containers filled with liquid against sudden excessive overpressure; however, the unstable vibration of a valve spool under dynamic loading may lead to safety incidents. This study aims to investigate the nonlinear vibration processes of a valve spool subjected to an underwater pressure pulse. To achieve this objective, the spring-loaded valve was simplified to an air-back mass spring with a constraint boundary (AMSCB). A modified split Hopkinson pressure bar (SHPB) was adopted to generate a controllable pressure pulse to establish the relationship between the specific impulse and the discharged water mass. Following the experimental verification, the influences of the pressure pulse parameters and dimensionless time on the motion characteristics of the mass block and flow rate were studied based on finite element (FE) simulations. Five motion modes were identified according to the number of collisions with the constraint boundary and changes in movement direction: (i) no collision, (ii) single collision, (iii) chatter, (iv) single collision with direction change, (v) multiple collisions. Moreover, a theoretical model for predicting the movement of a mass block was developed and validated against numerical results. The classification phase diagram of the motion mode is presented in a two-dimensional plane composed of specific strength coefficient ϕ and fluid-structure interaction coefficient ψ, and the influence of the geometrical parameters of the AMSCB on the classification boundary of motion modes is presented. The results indicate that, when subjected to underwater pressure pulse loading, the mass block repeatedly collides with the constraint boundary and undergoes non-periodic motion. With higher loading pressure amplitude and duration, the mass block is more likely to collide with the back boundary, leading to a transition in movement modes from mode (i), mode (ii), mode (iv) to mode (v). Increasing the stiffness coefficient and areal density will increase the threshold of ϕ and ψ for the transition from mode (i) to mode (v), while the maximum allowable displacement has little effect on the classification boundaries. These research findings are valuable for analysing the motion response of mass spring with various constraint boundaries under dynamic loading, and for guiding the design of spring-loaded valves.
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