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On the distribution of peaks and ranges of dynamic models of the linear and nonlinear responses of plates.

机译：关于板的线性和非线性响应的动力学模型的峰和范围的分布。

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摘要

The focus of this work is on the response of aircraft panels to random acoustic excitations and possible steady temperature effects. More specifically, the statistical distribution of the rainflow ranges of the response is analyzed in detail for an ensuing fatigue life estimation. A special emphasis is on high sound pressure levels situations for which the panel exhibits a strong, Duffing-type nonlinearity and significant membrane stresses inducing a quadratic relationship between displacements and stresses.;Two semi-empirical models are first proposed for the probability density function of the rainflow ranges which are based on the distributions of the peaks of displacement and stresses, respectively, of a one-mode model of the panel response. It is demonstrated that the simpler model, i.e. the one based on the peaks of displacements, provides an excellent fit of rainflow ranges obtained in simulation studies in a broad set of situations, except when the bending and membrane stresses are of comparable magnitudes. In such situations, the more complex model, based on peak of stresses, is shown to be accurate.;This modeling effort emphasized the need to better understand and predict the occurrence of small rainflow ranges. In the particular case of the response of a linear oscillator to white noise input, it was shown that there exist very close similarities between the distributions of the rainflow ranges and all peak-to-valley ranges both occurring in a given time interval τ, provided that τ is less than half a period. An approximate distribution of the values of τ is also proposed which displays the correct basic trends.;The peaks of the response envelope which could be expected to lead to particularly large rainflow ranges are finally studied. The envelope definition used primarily here is the amplitude process appropriately smoothed to remove any high frequency content. Relying on the stochastic averaging technique, an approximate expression is derived for the distribution of the peaks of the envelope for linear oscillators and a class of nonlinear ones. The excellent match between the expressions derived for both linear and Duffing oscillators and the corresponding results from Monte Carlo simulations validates the approach.
机译：这项工作的重点是飞机面板对随机声激励的响应以及可能的稳定温度影响。更具体地，详细分析响应的雨流范围的统计分布，以用于随后的疲劳寿命估计。特别强调的是在高声压级情况下，面板显示出强烈的Duffing型非线性和显着的膜应力，从而导致位移和应力之间呈二次关系。;首先提出了两个半经验模型来计算面板的概率密度函数降雨流量范围分别基于面板响应的单模模型的位移和应力峰值的分布。结果表明，较简单的模型（即基于位移峰值的模型）可以在广泛的情况下（通过模拟研究得出的结果）很好地拟合雨水流量范围，但当弯曲应力和膜应力的大小相当时除外。在这种情况下，基于应力峰值的更复杂的模型被证明是准确的。该建模工作强调需要更好地理解和预测小范围降雨的发生。在线性振荡器对白噪声输入的响应的特定情况下，表明在给定的时间间隔τ中，雨流范围的分布与所有峰谷范围的分布之间都存在非常相似的条件τ小于半个周期。还提出了τ值的近似分布，该分布显示了正确的基本趋势。最终研究了可以预期导致特别大的雨水流量范围的响应包络峰。这里主要使用的包络定义是经过适当平滑以去除任何高频成分的幅度过程。依靠随机平均技术，推导了线性振荡器和一类非线性振荡器的包络线峰值分布的近似表达式。从线性和Duffing振荡器导出的表达式与蒙特卡洛模拟的相应结果之间的出色匹配证明了该方法。

著录项

  • 作者

    Kim, Kwangkeun.;

  • 作者单位

    Arizona State University.;

  • 授予单位 Arizona State University.;
  • 学科 Engineering Mechanical.
  • 学位 Ph.D.
  • 年度 2005
  • 页码 153 p.
  • 总页数 153
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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