Fractional-order transfer function-based vibration transfer path analysis in satellite composite structures

This paper proposes a fractional-order damping mode superposition method within the framework of Transfer Path Analysis (TPA). The method is developed for the calculation of vibration transfer functions of composite structures deployed in ultra-quiet satellite platforms, with a view to accurately characterizing the vibration transfer properties of such structures. The conventional integer-order mode superposition method cannot precisely capture the frequency-dependent energy dissipation behavior of composite materials, and thus fails to satisfy the stringent requirements of high-precision structural design. To address this limitation, fractional-order damping terms are incorporated into the transfer function model, and an advanced non-classical numerical algorithm is employed for the high-precision and high-efficiency solution of fractional-order operators. The validity of the proposed method is verified by comparing its path transfer efficiency prediction accuracy with that of the integer-order mode superposition method and the Operational Transfer Path Analysis (OTPA) method. The similarity coefficients of the proposed method in the X, Y, and Z directions reach 0.9846, 0.9905, and 0.9815, respectively, surpassing the corresponding values of the integer-order method (0.8769, 0.8619, and 0.8255). It also outperforms the OTPA method, particularly in the high-frequency range (≥300 Hz). In addition, the transfer path contribution analysis enabled by this method identifies the dominant vibration propagation paths, laying a theoretical foundation for satellite vibration diagnosis and control. The results demonstrate that the proposed method enhances the computational accuracy of vibration transfer characteristics for composite materials and provides a robust tool for satellite micro-vibration control. It further broadens the applicability of TPA in the analysis of structures with complex material properties.