The analytical approach used in det

The analytical approach used in determining the response and
ultimately the fatigue behavior of panels exposed to the sound fields discussed earlier is an extension of Miles' work. The method uses the modal analysis results. i.e., normalized modal displacements and modal stresses. to obtain the load-deflection relationship. The effect of finite acoustic wavelengths on the panel response is incorporated through simultaneous consideration of spatial characteristics for both the structural modes and the sound field. Initially. the surface pressure distribution is approximated by the mass-weighted structural mode shape. For the fundamental mode of the panel, the estimate is similar to the assumption of uniform pressure. The advantage of this assumption is that it tends to produce a conservative estimate for each mode and the measure of spatial correlation (joint acceptance) between modal and acoustic fields is rendered unity. The accuracy of this approximation depends on the degree to which the mass-weighted mode shape reflects the actual pressure field shape. However, improvements to that joint acceptance estimate are developed which do not require detailed modeling of the acoustic field or numerical integration. This improvement is based on the relation between the structural and acoustic wavelengths. Thus, after a mode-by-mode evaluation of sonic stresses is performed initially, the joint acceptance correction detects and adjusts underpredicted and/or overpredicted sonic stress estimates. Finally, the overall stresses are obtained by summing the squares of contributions of the individual modes. A more detailed presentation of the analytical procedure is given in Reference [4-5]. Once the acoustically induced stresses have been determined, a direct comparison with available random fatigue data provides estimates for the number of mechanical cycles that can be sustained.

結果 (中文) 1:

用于确定响应的分析方法和最终疲劳的面板的行为暴露在前面讨论的声场是工作的英里的延伸。该方法利用模态分析的结果。即，归一化模态位移和应力的模态。要获取的荷载-挠度关系。通过结构模态与声场空间分布特征同时审议成立为法团小组反应中有限的声波波长的影响。最初。表面压力分布近似为质量加权结构振型。对于小组的基本模式，估计是类似于压力均匀的假设。这种假设的优点是它倾向于产生一个保守的估计，每个模式和模态和声学领域间的空间相关性 （联合验收） 的措施呈现统一。这种近似的准确性取决于质量加权模式形状反映实际压力场形状的程度。然而，对这一联合验收估计的改进被开发不需要详细的建模的声场或数值积分。这种改进基于结构和声波波长之间的关系。因此，声波应力模式的模式评价最初执行后，联合验收校正检测和调整 underpredicted 和/或 overpredicted 声波压力估计。最后，通过总结的贡献的各个模平方得到整体应力。分析方法的更详细介绍在文献 [4-5]。一旦确定了声学诱导的应力，可用随机疲劳数据进行直接比较提供可以持续的机械循环次数的估计数。

結果 (中文) 3:

用于确定响应和响应的分析方法最终暴露在前面讨论的声场的面板的疲劳行为是英里的工作的一个扩展。该方法采用模态分析结果。即，归一化模态位移和模态应力。获取荷载-挠度关系。有限的声波波长的面板响应的影响被纳入通过同时考虑的结构模式和声场的空间特性。最初。的表面压力分布近似的质量加权的结构模式形状。对于面板的基本模式，估计是相似的均匀压力的假设。这个假设的优点是，它往往会产生一个保守的估计，每个模式和空间相关（联合验收）之间的模态和声学领域的措施是统一的。这种近似的准确性取决于在该程度上的质量加权模式形状反映实际压力场形状。然而，改进的联合验收估计的开发，不需要详细的声场或数值积分的建模。这种改进是基于结构和声学波长之间的关系。因此，通过声波应力模式评价模式进行初步校正，联合验收检测和调整偏低或偏高的声波应力估算。最后，整体应力，通过总结的个别模式的贡献的平方。更详细的介绍的分析方法是在给定参考[4-5]。一旦诱发应力已确定，与现有的随机疲劳数据提供了一个直接的比较估计机械循环的次数，可以持续。