Equation for the evolution of trapped hydrogen in an elastic rod subjected to high-frequency harmonic excitation

The hydrogen-containing solid is assumed to consist of an elastic matrix with voids filled by hydrogen. This model is used for modeling the process of diffusion and trapping the hydrogen in an elastic rod subjected to high-frequency excitation. The differential equation for the trapped hydrogen concentration is obtained in the one-dimensional case. The method of direct separation of vibrational processes allows one to introduce the “fast” and “slow” components in the process of hydrogen redistribution in the material. The governing equation for the evolution of the trapped hydrogen concentration in the vibrating elastic rod is derived, and it reflects the considerable impact of high-frequency vibration on the evolution of trapped hydrogen. The resulting equation is shown to differ significantly from the original equation for the hydrogen concentration.