Response Energy Behavior and Blast Damage Assessment of Unconstrained Simplified Dynamic Systems Subject to Blast Loading

Objective: Understanding the response energy behavior of components in a dynamic system subject to blast loading is critical. The objective is to find the analytical relations between the response energy of free two degree of freedom (FTDOF) systems subject to blast loading and the parameters of the loading and the system itself so that the issues with damage assessment and response energy behavior can be resolved. Methods: Energy ratio (ER) is selected to capture the response energy behavior of system components. The energy scaling method is used, which has been effective in previous study for constrained single degree-of-freedom systems. FEA simulation and given experimental results are applied in verification. Results: Maximum response ER for FTDOF systems subject to blast loading is derived. Theoretical derivation and simulation reveal that response kinetic energy carried by any single mass alone out of two lumped masses in an elastic FTDOF system can be larger than the response kinetic energy of a rigid body system formed with any one of the two lumped masses alone subject to the same blast load. Proper mass ratio and timing are critical for the result. Further observations of a perfectly plastic FTDOF system and a simplified Hanssen pendulum system (SHPS) without allowing any disintegration demonstrates that the disintegration of the Hanssen pendulum system is the main reason for Hanssen’s unexpected results. This is not only supported by the observations in Hanssen’s experiment, but also reproducible with FEA simulation, in which 13% higher kinetic energy is observed due to the disintegration. FEA analysis also reveals that dishing and impulse amplification have no significant effects, less than 1.3% and 2% variations in the response energy of the simulated SHPS, respectively. However, the impulse amplification, which can directly impact response energy, is significant for light-weight objects or low-density low-resistance materials directly facing blast loading. For damage assessment, any FTDOF system can dynamically be converted into an equivalent single degree-of-freedom system. Conclusion: The energy scaling method is effective in deriving the response ER analytically and obtaining the method of damage assessment for FTDOF systems. Maximum response ER≥1 for FTDOF systems is significant different from single degree-of-freedom systems. The disintegration of the Hanssen pendulum system is the main reason of the unexpected experimental results. Careful integration and constraint of components for systems constructed with cladding layers are extremely important. Effects of dishing and impulse amplification are ignorable on SHPS. Light-weight objects or low-density low-resistance materials directly subject to blast loading can result in unexpected error in FEA simulation. The method of damage assessment for FTDOF systems is developed.