Modeling and characteristics analysis of stress wave propagation in density gradient rod

Density gradient materials are increasingly used in collision prevention and energy absorption structures, where their performance strongly depends on the propagation and attenuation of stress waves during impact. However, existing studies rarely account for the combined influence of density gradient and lateral inertia on wave dynamics. To address this gap, this work establishes a unified theoretical model for stress wave propagation in density gradient rods, incorporating both effects into the one-dimensional wave equation by integrating the Rayleigh–Love theory and the density distribution function. The wave equation is solved analytically using the Laplace transform, and the model is validated against waveform propagation tests and numerical simulations, showing close agreement. The results demonstrate that a positive density gradient amplifies the peak stress and accelerates wave propagation, while a negative density gradient attenuates the peak stress and delays propagation. These findings highlight the potential of density gradient design for waveform control, providing theoretical guidance for engineering applications in aerospace structures and protective systems.