A new theoretical basis for the bandwidth method and optimal power ratios for the damping estimation

Abstract

Using the well-known bandwidth formula and the half power bandwidth formula [R.E.D. Bishop, G.M.L. Gladwell, An investigation into the theory of resonance testing, Philosophical Transactions of the Royal Society of London A 255 (1963) 241–280], in particular, is the simplest way to estimate modal damping for engineers. By using the half power bandwidth formula, the damping factor is estimated to be approximately the half bandwidth at the half power points. One of the major limitations that restrict the use of this method is the coupling effect between closely spaced modes. In this paper, the dependence of the damping estimation accuracy on the selected power ratios is studied with both analytical and experimental data of frequency response functions. The results show that by selecting adequate power ratio values, the coupling effect can be minimized and the estimation accuracy can be significantly improved for closely spaced modes. A further improvement of accuracy can be obtained by applying the algorithm of mode isolation [H.P. Yin, D. Duhamel, Substraction technique and finite difference formulas for modal parameter estimation, Mechanical Systems and Signal Processing 18 (2004) 1497–1503; M.S. Allen, J.H. Ginsberg, A global, single-input-multi-output (SIMO) implementation of the algorithm of mode isolation and application to analytical and experimental data, Mechanical Systems and Signal Processing 20 (2006) 1090–1111]. Also an exact bandwidth formula in case of a single degree of freedom system is presented and the link between the exact formula and the classical approximated formula is indicated. The exact bandwidth formula provides a new theoretical basis of the bandwidth method for the damping estimation from frequency response functions.