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

机译：带宽方法的新理论基础和阻尼估计的最佳功率比

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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.
机译：使用众所周知的带宽公式和半功率带宽公式[R.E.D. G.M.L. Bishop Gladwell，《对共振测试理论的研究》，伦敦皇家学会的《哲学交流》 A 255（1963）241-280]，特别是估计工程师的模态阻尼的最简单方法。通过使用半功率带宽公式，可以估算出阻尼因子约为半功率点处的半带宽。限制使用此方法的主要限制之一是紧密模式之间的耦合效应。本文利用频率响应函数的分析和实验数据研究了阻尼估计精度对所选功率比的依赖性。结果表明，通过选择适当的功率比值，可以将耦合效应最小化，并且对于紧密间隔的模式，可以显着提高估计精度。通过应用模式隔离算法可以进一步提高精度。 Yin，D.Duhamel，用于模态参数估计的减法技术和有限差分公式，Mechanical Systems and Signal Processing 18（2004）1497-1503;多发性硬化症。艾伦（J.H. Ginsberg，模式隔离算法的全局，单输入多输出（SIMO）实现，以及对分析和实验数据的应用，《机械系统与信号处理》，第20期（2006）1090-1111]。还给出了单自由度系统情况下的精确带宽公式，并指出了精确公式与经典近似公式之间的联系。精确的带宽公式为根据频率响应函数进行阻尼估计的带宽方法提供了新的理论基础。

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