Adopting dynamic substructuring schemes is a common practice in the field of structural dynamics, where the dynamic behaviour of a structure is predicted by combining the multiple subsystems that are ...analysed individually. This paper investigated the dynamic behaviour of a structure with doubled bolted joints using the frequency based substructuring (FBS) method. In the attempt, the substructures were combined with the frequency domain that can be numerically derived or experimentally measured. However, the applicability of this method suffered from several issues where most of them were related to the frequency response function (FRF) of the rotational degree of freedom (DOF) at the subsystem’s interface. In some cases, the system’s interface vibrated in the rotary motion of certain modes, for instance, a car side rear view mirror. Therefore, excluding the rotational FRF during the coupling process could lead to a completely different result. This paper presents the use of the FBS method for a structure with double bolted joints by using the equivalent multipoint constraint (EMPC) method through which rotational DOFs can be completely neglected. The actual tested structure for this study was an assembled structure consisting of two substructures: a simple beam and an irregular plate steel structure. The FRFs of both substructures were derived from using the FRF synthesis from finite element models and combined together via the FBS method. This study reveals that the use of the FBS method with the EMPC method for a structure double bolted joints has led to very promising results.
In many cases, the use of damping technologies is the only option to reduce undesired vibrations. Despite various damping techniques available on the market, the design of a precise damping behaviour ...still needs a lot of experimental testing and engineering experience. This is also the case for particle damping. However, for lightweight structures, technologies such as particle damping provide an opportunity to improve the structural dynamic behaviour without a large mass gain. With respect to this conflict, a hybrid numerical and experimental design approach is presented based on frequency based substructuring (FBS). With this technique, the use of experimental data for design optimization is possible and detailed modelling of the nonlinear particle damping system can be avoided. Moreover, based on the FBS, an approach to optimize damping and weight is proposed. All results are compared to experiments, and a subsequent discussion shows that the predictions for particle damping with FBS are accurate for defined operating points from which realistic designs can be derived. Generally, it is shown that methodical design approaches may strongly improve not only product development processes but also structural mechanical design.
Combining analytical with experimental data to predict the dynamic behaviour of an assembled structure via the frequency based substructuring (FBS) method, is a common practice in the field of ...structural dynamics. However, the accuracy of the dynamic behaviour predicted from the FBS method relies heavily on the quality of experimental frequency response function (FRF) of the interfaces on which, in practice, it is very difficult to obtain. In addition, the accuracy of the FBS method is highly dependent on experimental rotational degrees of freedom (DOF) which are always found to be very difficult to measure accurately. Therefore, this paper proposes a new frequency response function (FRF) coupling scheme that may uniquely address the difficulties and improve the quality of predicted results of the FBS method. The scheme is formulated based on the finite element method, model updating technique and experimental modal analysis. A simplified finite element model of a physical test substructure is developed to generate rotational FRF data by reconciling the initial FE model using the model updating technique. It was found that the scheme adopted allows generating full translational and rotational degrees of freedom data and leads to a significant improvement in the FRF coupling process between the analytical and experimental model in the FBS method.
The traditional way of low stiffness suspension may no longer work for very large scale structures with extremely low first flexible natural frequency. In this paper, we replace the low stiffness ...suspension with a group of supports. After separate Frequency Response Function tests of the whole supported structure and the support structures, the influence of the supports could be removed from a later computation. To this end, the identification method and support design are critical. The existing substructure decoupling methods are briefly reviewed and some incomplete issues in the earlier works are discussed. Then the relationship among the methods is investigated. With these studies, some improvements on the pseudo-force method are made. The proper design of supports and measurement locations are also studied. Both numerical and experimental examples are described in the paper.
•The best identification formulae of the ‘negative structure’ method are found.•Requirements on the decoupling DOFs are given mathematically.•The pseudo-force method is extended to the cases of lacking interface information.•A criterion is given to design the support and place the measurement points.
Frequency-based substructuring is a very popular approach for the generation of system models from component measured data. Analytically the approach has been shown to produce accurate results. ...However, implementation with actual test data can cause difficulties and cause problems with the system response prediction. In order to produce good results, extreme care is needed in the measurement of the drive point and transfer impedances of the structure as well as observe all the conditions for a linear time invariant system.
Several studies have been conducted to show the sensitivity of the technique to small variations that often occur during typical testing of structures. These variations have been observed in actual tested configurations and have been substantiated with analytical models to replicate the problems typically encountered. The use of analytically simulated issues helps to clearly see the effects of typical measurement difficulties often observed in test data.
This paper presents some of these common problems observed and provides guidance and recommendations for data to be used for this modeling approach.
Frequency based substructuring approaches have been used for the generation of system models from component data. While numerical models show successful results, there have been many difficulties ...with actual measurements in many instances. Previous work has identified some of these typical problems using simulated data to incorporate specific measurement difficulties commonly observed along with approaches to overcome some of these difficulties.
This paper presents the results using actual measured data for a laboratory structure subjected to both analytical and experimental studies. Various commonly used approaches are shown to illustrate some of the difficulties with measured data. A new approach to better condition the measured functions and purge commonly found data measurement contaminants is utilized to provide dramatically improved results.
Several cases are explored to show the difficulties commonly observed as well as the improved conditioning of the measured data to obtain acceptable results.
Dynamic substructuring offers the possibility to simulate assembled systems efficiently. The coupling of the substructures can be established either by Component Mode Synthesis (CMS), or Frequency ...Response Functions (FRF) can be used to couple the substructures by Frequency Based Substructuring (FBS). In real systems, coupling is done by joints which can influence the dynamics of the assembled system significantly due to local damping and nonlinearities caused by friction. In this contribution the coupling of two beam-like substructures, which are assembled by a bolted joint, is considered using both coupling methods. While the substructures are linear, the implementation of the nonlinear friction forces requires special attendance in the equations of motion. The Harmonic Balance Method is therefore used to efficiently compute FRFs. Using FBS, the coupling is established directly in the frequency domain. The method provides the possibility to replace the dynamics of individual substructures by measured FRFs of the uncoupled system and combining numerical and experimental models. Alternatively, Component-Mode-Synthesis is used.
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