Ignoring rotational DoFs in decoupling structures connected through flexotorsional joints

Substructure decoupling consists in the identification of the dynamic behaviour of a structural subsystem, starting from the dynamic behaviour of both the assembled system and the residual subsystem (the known portion of the assembled system). The degrees of freedom (DoFs) of the coupled system can be partitioned into internal DoFs (not belonging to the couplings) and coupling DoFs. In direct decoupling, a fictitious subsystem that is the negative of the residual subsystem is added to the coupled system, and appropriate compatibility and equilibrium conditions are enforced at interface DoFs. Compatibility and equilibrium can be required either at coupling DoFs only (standard interface), or at additional internal DoFs of the residual subsystem (extended interface), or at some coupling DoFs and some internal DoFs of the residual subsystem (mixed interface). In this paper, a test bench is considered made by a cantilever column with two staggered short arms coupled to a horizontal beam. This involves both flexural and torsional DoFs, on which rotational FRFs are quite difficult to measure. Using a mixed interface, rotational DoFs are neglected and substituted by internal translational DoFs. Experimental results are presented and discussed

Dynamic Model Updating Using Virtual Antiresonances

This paper considers an extension of the model updating method that minimizes the antiresonance error, besides the natural frequency error. By defining virtual antiresonances, this extension allows the use of previously identified modal data. Virtual antiresonances can be evaluated from a truncated modal expansion, and do not correspond to any physical system. The method is applied to the Finite Element model updating of the GARTEUR benchmark, used within an European project on updating. Results are compared with those previously obtained by estimating actual antiresonances after computing low and high frequency residuals, and with results obtained by using the correlation (MAC) between identified and analytical mode shapes

Substructure decoupling without using rotational DoFs: fact or fiction?

In the framework of experimental dynamic substructuring, substructure decoupling consists in the identification of the dynamic behaviour of a structural subsystem, starting from the dynamic behaviour of both the assembled system and the residual subsystem (the known portion of the assembled system). On the contrary, substructure coupling identifies an assembled system starting from the component subsystems. The degrees of freedom (DoFs) of the assembled system can be partitioned into internal DoFs (not belonging to the couplings) and coupling DoFs. In substructure coupling, whenever coupling DoFs include rotational DoFs, the related rotational FRFs must be obtained experimentally. Does this requirement holds for substructure decoupling too, as it is commonly believed? Decoupling can be ideally accomplished by adding the negative of the residual subsystem to the assembled system (direct decoupling) and by enforcing compatibility and equilibrium at enough interface DoFs. Ideally, every DoF of the residual subsystem belongs to the interface between the assembled system and the residual subsystem. Hopefully, not all the coupling DoFs are necessary to enforce compatibility and equilibrium. This may allow us to skip coupling DoFs and specifically rotational DoFs. The goal of the paper is indeed to establish if rotational FRFs at coupling DoFs can be neglected in substructure decoupling. To this aim, after highlighting the possibility of avoiding the use of coupling DoFs from a theoretical standpoint, a test bed coupled through flexural and torsional DoFs is considered. Experimental results are presented and discussed

Vibroacoustic optimization using a statistical energy analysis model

In this paper, an optimization technique for medium-high frequency dynamic problems based on Statistical Energy Analysis (SEA) method is presented. Using a SEA model, the subsystem energies are controlled by internal loss factors (ILF) and coupling loss factors (CLF), which in turn depend on the physical parameters of the subsystems. A preliminary sensitivity analysis of subsystem energy to CLFs is performed to select CLFs that are most effective on subsystem energies. Since the injected power depends not only on the external loads but on the physical parameters of the subsystems as well, it must be taken into account under certain conditions. This is accomplished in the optimization procedure, where approximate relationships between CLFs, injected power and physical parameters are derived. The approach is applied on a typical aeronautical structure: the cabin of a helicopter

Selection of Interface DoFs in Hub-blade(s) Coupling of Ampair Wind Turbine Test Bed

International audienceSubstructure coupling is an important tool in several applications ofmodal analysis. It is particularly relevant in virtual prototyping of complex systems and responds to actual industrial needs, especially in an experimental context. Furthermore, the reverse problem, the decoupling of a substructure from an assembled system, arises when a substructure cannot be tested separately but only when coupled to neighboring substructures, a situation often encountered in practice. In this paper, the dynamic behavior of the Ampair test bed wind turbine rotor, made by three blades - each one bolted to the hub at three points - is analyzed. The aim is both to identify the dynamic behavior of the rotor starting from the frequency response functions (FRFs) of blades and hub, and to select a reduced set of relevant DoFs to represent the interface between blades and hub. FRFs to be used in the coupling procedure are obtained starting from FE model of each substructure, by using a super-element based computational approach. The decoupling problem, with the aim of identifying the dynamic behavior of each blade from the FRFs of the assembled rotor and of the hub, is also considered

Identification of bolted joint properties through substructure decoupling

Substructure decoupling techniques, defined in the frame of Frequency Based Substructuring, allow to identify the dynamic behaviour of a structural subsystem starting from the known dynamics of the coupled system and from information about the remaining components. The problem of joint identification can be approached in the substructuring framework by decoupling jointed substructures from the assembled system. In this case, information about the coupling DoFs of the assembled structure is necessary and this could be a problem if the interface is inaccessible for measurements. Expansion techniques can be used to obtain the dynamics on inaccessible (interface) DoFs starting from accessible (internal) DoFs. A promising technique is the System Equivalent Model Mixing (SEMM) that combines numerical and experimental models of the same component to obtain a hybrid model. This technique has been already used in an iterative coupling–decoupling procedure to identify the linear dynamic behaviour of a joint, with a Virtual Point description of the interface. In this work, a similar identification procedure is applied to the Brake Reus Beam benchmark to identify the linear dynamic behaviour of a three bolted connection at low levels of excitation. The joint is considered as a third independent substructure that accounts for the mass and stiffness properties of the three bolts, thus avoiding singularity in the decoupling process. Instead of using the Virtual Point Transformation, the interface is modelled by performing a modal condensation on remote points allowing deformation of the connecting surfaces between subcomponents. The purpose of the study is to highlight numerical and ill-conditioning problems that may arise in this kind of identification

Strategies to exploit test data in subsystem subtraction

In dynamic substructuring, the subtraction of subystems (decoupling) is a very critical problem even in apparently trivial applications. Using simulated FRF data, it has been highlighted that - as predicted by the theory - the solution of decoupling problems is affected by ill-conditioning around a discrete number of frequencies, and is dependent on the choice of the 'measured DoFs'. In experimental dynamic substructuring, additional problems can arise (systematic errors, inconsistencies, etc.) that are strictly connected with the use of measured FRFs, and different strategies to obtain reliable results can be necessary. In this paper, experimental data, acquired on a test bed made by a plate and a rigid mass, are used to check the decoupling procedure and to look for additional issues that can not be observed from simulated data. © The Society for Experimental Mechanics, Inc. 2014

Reducing variability of a set of structures assembled from uncertain substructures

In this paper, the effect of component variability (due for instance to dimensional tolerances) on the dynamics of an assembled structure is modeled using procedures derived from Design of Experiments (DOE). Central composite design is used to fit a regression model of the effect of uncertainties and of their interactions. The regression model is verified by comparing the output of the fitted model with results of the physical model. The fitted model is then used instead of the physical model to evaluate the dynamic behaviour of the assembled structure. A reduced fitted model is defined by taking into account only the contribution of most significant uncertainties. By using the reduced fitted model, selective assembly procedures are devised in order to reduce the dynamic variability of a set of assembled structures

Frequency based subsystem identification using hybrid primal-dual formulation

The paper considers the identification of a structural subsystem, starting from the Frequency Response Functions of the assembled system, and from information about the remaining part of the structural system (residual subsystem), i.e. the so called decoupling problem. A possible approach is direct decoupling, which consists in adding to the coupled system a fictitious subsystem which is the negative of the residual subsystem. Starting from the 3-field formulation (dynamic balance, compatibility and equilibrium at the interface), the problem can be solved in a primal or in a dual manner. Compatibility and equilibrium can be required either at coupling DoFs only, or at additional internal DoFs of the residual subsystem. Furthermore DoFs used to enforce equilibrium might be not the same as DoFs used for compatibility: this generates the so called non collocated approach. In this paper, a hybrid primal-dual formulation is applied in combination with collocated and non collocated interface. © 2011 by ASME