Development of a hybrid FE-SEA-experimental model

Abstract

The vibro-acoustic response of complex structures with uncertain properties is a problem of great concern for modern industries. In recent years, much research has been devoted to the prediction of this response in the mid-frequency range where, because neither finite element analysis nor statistical energy analysis are appropriate, a hybrid deterministic-statistical approach becomes a suitable solution. Despite its potential, the existence of systems with active components that are too complex to be modelled numerically can limit the application of the method. However, it may still be possible to measure the dynamical response of these structures experimentally. This paper is hence concerned with the possibility of integrating experimental data into a hybrid deterministic-statistical method. To explain the new methodology, two similar case studies, consisting of a deterministic source structure that is coupled to a statistical plate receiver using passive isolators, are used. For each case, the vibratory excitation, characterised using in-situ blocked force measurements, the source structure mobility, and the isolators stiffness are experimentally determined and inserted in the proposed hybrid model of the system. The paper explains the techniques used for obtaining the considered experimental data and the theoretical model proposed for describing the systems.To validate the proposed approach, the predicted vibration response of the receiver plate is compared to the one obtained by experimentally randomising the plate in both case studies. The results show that a good agreement is obtained, both for the ensemble average response of the receiver structure and for the ensemble variance of this response. Moreover, the upper confidence bounds predicted by the hybrid method enclose well the ensemble of experimental results. The cause of some narrow-band differences observed between the predicted response and the experimental measurements is finally discussed. It is therefore concluded that the capabilities of the hybrid deterministic-statistical method can be clearly enhanced through the incorporation of experimental data prescribing active sub-systems.

Evaluation of Uncertainties in Classical and Component (Blocked Force) Transfer Path Analysis (TPA)

“…For example, if there are temperature changes or if operating loads cause changes in the FRFs then then operational and FRF measurement actually describe slightly different systems. It was shown in [10,11] that this can result in significant errors in certain frequency ranges. This can be illustrated by expressing the measured operational acceleration in terms of the 'true' force (or blocked force), f true , and the true FRF matrix, Y true .…”

“…The procedure for calculating uncertainties can be summarized by substituting equation (11) into equation 9:…”

A hybrid meshless–statistical energy analysis method for complex structure vibration analysis

“…Wu introduced an embedding of the gradient smoothing technique to the FE-SEA framework, which leads to much more accurate results in numerical cases [29]. Clot proposed a hybrid FE-SEA-experimental model in which some of the structural parameters are determined by experimental data [30,31]. Besides the deterministic methods mentioned above, another numerical method, i.e., the meshless method (MM), has rapidly increased popularity in the last 30 years and developed in a large class of numerical methods.…”

An experimental exploration of the properties of random frequency response functions

“…The use of experimental data to extend the capabilities of hybrid FE-SEA models was recently studied in [10]. The work develops a case study which includes complex vibration sources that have been represented using experimental blocked forces [11], and resilient elements that have been experimentally characterised [12].…”