The flexible positioning platform is a critical structural component in the ultra-high acceleration macro–micro motion platform, enabling precise positioning across multiple scales. However, under high-frequency start–stop cycles and prolonged multi-condition operation, it is prone to fatigue damage induced by random vibrations, which poses a threat to system reliability. This study proposes a method for evaluating and optimizing the platform’s performance under random vibration based on power spectral density (PSD) analysis. In accordance with the IEC 60068-2-64 standard, representative load spectra from Tables A.8 and A.6 were selected as excitation inputs. Frequency-domain analyses of stress, strain, and displacement were conducted using ANSYS Workbench 2022R1 in conjunction with the nCode platform, incorporating the Gaussian three-sigma probability interval. The results reveal that stress and deformation are highly concentrated in the hinge region, indicating a structural vulnerability. Fatigue life predictions were carried out using the Dirlik method and Miner’s linear damage rule under various PSD loading conditions. The findings demonstrate that hinge stiffness is a key factor influencing vibration resistance and service life. This research provides theoretical support for the design optimization of flexible structures operating in complex random vibration environments.
Zhang et al. (Tue,) studied this question.