Abstract
A bandwidth method based on power ratio is proposed to evaluate the system damping by using frequency response functions. For single-degree freedom systems, exact formula for calculating damping ratio from displacement frequency response function is established. Additionally, an approximate formula to estimate the damping ratio from acceleration frequency response function is also derived. Both are represented in terms of the power ratio and the bandwidths relative to the corresponding peak frequencies. In contrast to the well-known half-power method, the proposed method can be used for relatively large damping ratios by selecting a corresponding high power ratio. The accuracy of the proposed formulas in damping estimation is investigated for a four-degree of freedom system by numerical experiments. The results show that by increasing the power ratio, the estimation errors in damping ratios for the four-degree of freedom system can be significantly reduced.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ewins, D.J.: Modal Testing: Theory, Practice and Application, 2nd edn. Research Studies Press, England (2000)
Thomson, W.T.: Theory of Vibration with Applications, 4th edn. Prentice-Hall, New Jersey (1993)
Chopra, A.K.: Dynamics of Structures, 3rd edn. Prentice Hall, New Jersey (2007)
Stembalski, M., Skoczyński, W., Roszkowski, A., Preś, P.: Testing the vibration damping of a glass gatherer robot arm using a friction damper. Arch. Civ. Mech. Eng. 17(2), 240–248 (2017)
Olmos, B.A., Roesset, J.M.: Evaluation of the half-power bandwidth method to estimate damping in systems without real modes. Earthq. Eng. Struct. Dyn. 39(14), 1671–1686 (2010)
Wang, I.: An analysis of higher order effects in the half power method for calculating damping. ASME J. Appl. Mech. 78(1), 014501 (2011)
Papagiannopoulos, G.A., Hatzigeorgiou, G.D.: On the use of the half-power bandwidth method to estimate damping in building structures. Soil Dyn. Earthq. Eng. 31(7), 1075–1079 (2011)
Wang, J.T., Jin, F., Zhang, C.H.: Estimation error of the half-power bandwidth method in identifying damping for multi-DOF systems. Soil Dyn. Earthq. Eng. 39(8), 138–142 (2012)
Wang, J.T., Lü, D.D., Jin, F., Zhang, C.H.: Accuracy of the half-power bandwidth method with a third-order correction for estimating damping in multi-DOF systems. Earthq. Eng. Eng. Vib. 12(1), 33–38 (2013)
Chandra, N.H., Sekhar, A.S.: Swept sine testing of rotor-bearing system for damping estimation. J. Sound Vib. 333(2), 604–620 (2014)
Wu, B.: A correction of the half-power bandwidth method for estimating damping. Arch. Appl. Mech. 85(2), 315–320 (2015)
Yin, H.P.: A new theoretical basis for the bandwidth method and optimal power ratios for the damping estimation. Mech. Syst. Signal Process. 22(8), 1869–1881 (2008)
Acknowledgements
This research was supported in part by the National Natural Science Foundation of China (Grant Nos. 11672118 and 91648108).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wu, B., Liu, W. & Wu, X. A damping estimation method based on power ratio. Arch Appl Mech 88, 1919–1927 (2018). https://doi.org/10.1007/s00419-018-1434-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-018-1434-2