Mechanical structures are often subjected to random vibrations due to external forces (forces, acceleration...). Improving the safety of structures and reducing manufacturing and design costs is achieved thanks to accurate fatigue design methods. The first part of the thesis consisted in the establishment of a state of the art on design methods for fatigue under vibrational environment. The mathematical representation of random vibration, conventional fatigue design methods for uniaxial and multiaxial loads as well as fatigue design methods formulated in the spectral domain have been thoroughly studied. The latter have been applied to random vibrations cases, through a number of assumptions. They show significantly lower computation time than conventional design methods. The second part of the thesis is the development of a fatigue design method formulated in the spectral domain, which is valid over the whole domain of fatigue, from low cycle fatigue (LCH) to high cycle fatigue (HCF). The work focused on the integration of confined elasto-plastic behaviour of the materials in spectral methods. The proposed approach has been the subject of a comparative numerical study with existing methods. The last part of the thesis presents the comparison of proposed method to physical tests. A test specimen specific to this study has been developed. The results show a good correlation between the numerical and experimental approaches.
