Vibration analysis of heavy weapons in transit by aircraft in fractal space considering location deviation

Air transportation constitutes a significant advancement in enhancing transportation efficiency. Nonetheless, when this modality is employed for the transit of large-scale armaments and equipment, the vibrational properties of these items within the aircraft's cabin, coupled with potential deviations from their designated installation positions, emerge as critical factors that could compromise the safety of such transportation endeavors. To accommodate the unique environmental conditions of low-temperature and low-pressure prevalent in high-altitude air transportation, this model employs a fractal frequency formula for an expedited and accurate characterization of vibrational properties, while also providing a detailed analysis of the errors attributable to positional deviations in these vibration assessments. The findings of this research demonstrate that the computational accuracy achieved herein surpasses that of the variational iteration method (VIM) and the homotopy perturbation method (HPM). Moreover, the investigation into the damping effects of inertial forces within fractal dimensions unveils innovative prospects for optimizing nonlinear vibration systems under the challenging conditions of low-temperature and low-pressure environments.