In response to the protection against random vibration damage during road transportation of missiles, the work aims to establish a coupled dynamics model of the missile-packaging container-cushioning liner and adopt Differential Evolution (DE) and Particle Swarm Optimization (PSO) to optimize the cushioning parameters, providing a theoretical basis and design reference for the cushioning protection of missile packaging containers. Based on the GJB 150.16A-2009 standard, the frequency-domain filtering method was used to synthesize random vibration acceleration time histories in line with road transportation requirements. Both a three-degree-of-freedom (MDOF) model and a single-degree-of-freedom (SDOF) model were established, taking into account the three-dimensional weak coupling effect caused by the offset of the missile’s center of gravity. Three types of cushioning materials, including expanded polyethylene (EPE), expanded polystyrene (EPS), and honeycomb cardboard were selected, and their mechanical behavior was described by cubic polynomials. The Newmark-β method was adopted for time-domain integration, and Monte Carlo simulation was used for statistical analysis of the results. Two global optimization algorithms, DE and PSO, were respectively applied to search for the optimal stiffness-damping combination, with a static load-bearing constraint introduced into the optimization model to ensure engineering feasibility. The vibration-damping performance of the three cushioning materials exhibited an acceleration-displacement trade-off. Taking comprehensive account of the requirements for reusability, cleanliness, and environmental adaptability, EPE was selected as the base material for parameter optimization. After optimization, the peak acceleration decreased to 1.14g (a reduction of approximately 50.2%), the root-mean-square (RMS) acceleration decreased to 0.245g (a reduction of approximately 43.8%), and the maximum displacement decreased to 7.81 mm. Under the material parameters and excitation conditions investigated in this work, the hardening-type cubic nonlinear model can effectively describe the dynamic behavior of foam materials during the densification stage. The optimized cushioning parameters significantly reduce the acceleration response.
Key words
missile packaging container /
random vibration /
GJB 150.16A /
Newmark-beta method /
cushioning optimization /
differential evolution (DE) /
particle swarm optimization (PSO)
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