Abstract The vibro-acoustic analysis of complex structures over a broadband frequency range is an extremely challenging problem that may often require the use of a hybrid deterministic-statistical approach. Due to manufacturing imperfections, the frequency response functions (FRFs) of an ensemble of nominally identical systems can be considered to be random. These FRFs, however, have statistical properties that can be potentially used in vibro-acoustic models. This work explores some of these fundamental properties by using measured FRFs from an ensemble of nominally identical structures, obtained by randomising a thin rectangular plate using point masses. It is first shown that the measured ensemble of FRFs satisfies the analyticity-ergodicity condition, experimentally verifying this recently demonstrated fundamental property. Then, the ensemble is used to explore whether the direct field dynamic stiffness, a key parameter in a well-established hybrid deterministic-statistical formulation, can be obtained experimentally. The results are compared against those computed using numerical techniques, showing that measured data may be a suitable alternative provided that an ensemble of systems can be measured. Finally, an alternative method, based on the use of virtual point masses, opposed to physical ones, is proposed for those cases where experimental randomisation is particularly challenging. It has been found, however, that the method may be extremely sensitive to measurement imprecisions, specially when applied to lightly damped structures. It is concluded that the statistical properties of random causal FRFs are not only interesting in themselves, but can enhance and extend vibro-acoustic prediction models.

中文翻译：

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随机频率响应函数性质的实验探索

摘要 在宽带频率范围内对复杂结构进行振动声学分析是一个极具挑战性的问题，通常需要使用混合确定性统计方法。由于制造缺陷，名义上相同的系统集合的频率响应函数 (FRF) 可以被认为是随机的。然而，这些 FRF 具有可用于振动声学模型的潜在统计特性。这项工作通过使用来自名义上相同结构的集合的测量 FRF 来探索这些基本特性中的一些，这些结构是通过使用点质量随机化薄矩形板而获得的。首先表明，FRF 的测量集合满足分析性-遍历性条件，通过实验验证了最近证明的这一基本性质。然后，该集成用于探索是否可以通过实验获得直接场动态刚度，这是一个完善的混合确定性 - 统计公式中的关键参数。结果与使用数值技术计算的结果进行比较，表明如果可以测量系统集合，则测量数据可能是合适的替代方案。最后，针对那些实验随机化特别具有挑战性的情况，提出了一种基于使用虚拟点质量而不是物理点质量的替代方法。然而，已经发现该方法可能对测量不精确度极其敏感，特别是当应用于轻阻尼结构时。得出的结论是，随机因果 FRF 的统计特性不仅本身有趣，