The approximate calculation of the natural frequencies of a Stockbridge type vibration damper and analysis of natural frequencies' sensitivity to the structural parameters

Abstract. Vibration damper is widely used in overhead transmission lines to alleviate aeolian vibration. Its natural frequencies are important parameters for a vibration damper. In this paper, the approximate calculation formulas of natural frequencies of the one-side subsystem of a Stockbridge type vibration damper were derived and the design sensitivity analysis of the natural frequencies was studied using partial differential equations with respect to each concerned parameter including the length of the steel strand, the mass of the counterweight, the eccentric distance, and the radius of gyration of the counterweight. Through a case study that considered a variation of up to ±30  % in the values of the design parameters, the exact calculation and approximate calculation results of the natural frequencies were analysed, and the sensitivity of the vibration damper's natural frequencies to the design parameters was studied. The results show that, within the range of the parameters used in this study, the approximately calculated first-order frequency is lower than the exact values, whereas the approximately calculated second-order frequency is larger than the exact values. The sensitivity analysis indicates that the first-order frequency is highly sensitive to the steel strand's length, whereas it is moderately sensitive to the counterweight's mass and slightly sensitive to the eccentric distance and the gyration radius of the counterweight; the second-order frequency is highly sensitive to the steel strand's length and the gyration radius of the counterweight, moderately sensitive to the counterweight's mass, and slightly sensitive to the eccentric distance. It will provide theoretical guidance and approximate analysis method in engineering for the design of the vibration damper.