A recursive coupling-decoupling approach to improve experimental frequency based substructuring results

Substructure decoupling techniques allow identifying the dynamic behavior of a substructure starting from the dynamic behavior or the assembled system and a residual subsystem. Standard approaches rely on the knowledge of all FRFs at the interface DOFs between the two substructures. However, as these typically include also rotational DOFs which are extremely difficult and most of the time impossible to measure, several techniques have been investigated to overcome these limitations. A very attractive solution consists in defining mixed or pseudo interfaces, that allow to substitute unmeasurable coupling DOFs with internal DOFs on the residual substructure. Additionally, smoothing/denoising techniques have been proposed to reduce the detrimental effect of FRF noise and inconsistencies on the decoupling results. Starting from these results, some recent analysis on the possibility of combining coupling and decoupling FBS to validate the results and compensate for inconsistencies will be presented in this paper. The proposed method relies on errors introduced in the substructuring process when assuming that the interface behaves rigidly, while it is generally known that this assumption is seldom verified. Consequently, a recursive coupling-decoupling approach will be used to improve the estimation of the dynamic response of either the residual structure (for decoupling) or the assembly (for coupling). The method, validated on analytical data, will be here analyzed on a numerical example inspired by an experimental campaign used to validate the finite element models and on which standard substructuring techniques showed some limitations. The results discussed in this paper will be then used as guidelines to apply the proposed methodologies on experimental data in the future

Evaluation of different contact assumptions in the analysis of friction-induced vibrations using dynamic substructuring

Dynamic substructuring methods are initially developed for time-invariant systems to evaluate the dynamic behavior of a complex structure by coupling the component substructures. Sometimes, the component substructures change their position over time, affecting the dynamics of the entire structure. This family of problems can be tackled using substructuring techniques by isolating the time dependency in the coupling conditions among the time-invariant substructures. Mechanical systems, composed of subsystems in relative motion with a sliding interface, can be analyzed using this approach. In previous work, the authors proposed a solution method in the time and frequency domain using this approach under the assumption that the relative sliding motion at the contact interfaces is a-priori known, at least approximately. This assumption implies that the perturbation generated by the friction-induced vibration is neglected. In subsequent work, a more realistic contact assumption was considered to account also for the local vibration of the contact point and the geometric nonlinearity due to the elastic deformation. In this paper, a simplification with respect to the realistic contact assumption is introduced, which neglects the angular variation of the direction normal to the contact interface. The simplified approach is advantageous because it is equally able to highlight the occurrence of friction-induced instabilities, and it reduces the computational burden. The results of the substructuring methods using different contact assumptions are compared with those of a reference numerical method to show how the choice of the contact algorithm allows for tackling a wide range of operating conditions, from simple position-dependent problems up to complex friction-induced vibration phenomena

Friction-induced vibrations in the framework of dynamic substructuring

In complex vibrating systems, contact and friction forces can produce a dynamic response of the system (friction-induced vibrations). They can arise when different parts of the system move one with respect to the other generating friction force at the contact interface. Component mode synthesis and more in general substructuring techniques represent a useful and widespread tool to investigate the dynamic behavior of complex systems, but classical techniques require that the component subsystems and the coupling conditions (compatibility of displacements and equilibrium of forces) are time invariant. In this paper, a substructuring method is proposed that, besides accounting for the macroscopic sliding between substructures, is able to consider also the local vibrations of the contact points and the geometric nonlinearity due to the elastic deformation, by updating the coupling conditions accordingly. This allows to obtain a more reliable model of the contact interaction and to analyze friction-induced vibrations. Therefore, the models of the component substructures are time invariant, while the coupling conditions become time dependent and a priori unknown. The method is applied to the study of a finite element model of two bodies in frictional contact, and the analysis is aimed to the validation of the proposed method for the study of dynamic instabilities due to mode coupling

Nonlinear substructuring in the modal domain: numerical validation and experimental verification in presence of localized nonlinearities

In many systems of interest, most of the structure is well approximated as linear but some parts must be treated as nonlinear to get accurate response predictions: significant nonlinear effects are due to the connections between coupled subsystems, such as in automotive or aerospace structures. The present work aims at predicting the nonlinear behavior of coupled systems using a substructuring technique in the modal domain. This study focuses on the effects of nonlinear connections on the dynamics of an assembly in which the coupled subsystems can be considered as linear. Each connection is instead considered as a quasi-linear substructure with stiffness that is function of amplitude or energy. The iterative procedure used here is enhanced with respect to previous works by enforcing a better control of the total energy at each iteration allowing to obtain the solution for a prescribed set of energy levels. Also, the initial guess and the convergence criterion have been modified to speed up the procedure. This technique is applied to a system made of two continuous linear subsystems coupled by nonlinear connections. The numerical results of the coupling are first compared to the ones obtained by using the Harmonic Balance technique on the model of the complete assembly to evaluate its effectiveness and understand the effects of modal truncation. Besides, a nonlinear connecting element, specifically designed in order to have a nearly cubic hardening behavior, is used in an experimental setup. Substructuring results are compared to experimental results measured on the assembled system, in order to evaluate the correlation between mode shapes and the accuracy in the resonance frequency at several excitation levels

Development of a digital twin for a hydraulic, active seat suspension system

The vibrations induced by the soil irregularities and other equivalent disturbances on agricultural tractors represent a major cause of disease for tractor drivers. The reduction of vibration exposure of operators is a topic of interest for the (Italian) National Institute for Insurance against Accidents at Work (INAIL). Several passive, semi-active, and active solutions are commercially available for the seat or the cabin suspension to isolate the driver from the vibrations. A prototype of a hydraulic active suspension system for the operator seat has been developed in the laboratories of INAIL. In this paper, nonlinear multi-physics modeling of the prototype has been carried after an experimental identification of the actuation system and specifically of the control valve parameters. The model is adjusted to retrace the system’s response and is used as a digital twin of the physical prototype to develop and optimize the control system. An equivalent simplified model is obtained to design a proper control strategy for the active suspension system. Finally, the controller is tested on the digital twin of the system to assess its performance in isolating vibrations

Prediction of substructure properties using decoupling procedures

In this paper the decoupling problem, i.e. the identification of the modal properties of a substructure that is part of a larger structure, is considered. The dynamic behaviour of the whole structure, in terms of Frequency Response Functions (FRFs) at the joints, is assumed to be known, together with the physical (finite element) model of the second substructure. The decoupling procedure recalls the FRFs based structural modification procedure. If the coupling conditions include rotational DoFs, an expansion of the experimental degrees of freedom is necessary to match theoretical and experimental data. The procedure is applied to a simply connected structure using both simulated and experimental test data

Antirisonanze virtuali per la correzione di modelli ad elementi finiti di sistemi vibranti

In this paper an extension of the model updating method is considered that minimizes the antiresonance error, together with 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

A comparison between the use of physical parameters and correction factors in dynamic model updating

The selection of quantities and/or variables that have to be corrected during the updating process is addressed in this paper. Among quantities, the major alternative is the choice between correction factors and physical parameters. The former represent scale factors used to adjust mass and stiffness submatrices of the analytical model, while the latter include parameters such as the elasticity modulus, mass density, geometrical dimensions, etc. Advantages and limitations in the process of updaring physical parameters instead of correction factors are highlighted: it can be shown that only a limited number of physical parameters can be simultaneously updated for each element. The two approaches are compared using a previously developed updating procedure to solve an experimental test case

Diritti edificatori e governo del territorio : un confronto tra riviste

Il 27 novembre 2014 nelle sede di Ca’ Tron dell’Università IUAV di Venezia, Archivio di Studi Urbani e Regionali ha organizzato un incontro di discussione su “Diritti edificatori e governo del territorio”. Un tema rilevante ancora al centro della riflessione sulle pratiche e sugli strumenti per il governo del territorio che continua a suscitare interesse, riflessioni transdisciplinari, opinioni e valutazioni discordanti e che meritava la costruzione di un incontro che ne mettesse in luce le potenzialità, i limiti, gli aspetti innovativi, i vincoli dati da alcune problematiche che in Italia non hanno trovato soluzione né sul piano giuridico tantomeno su quello politico. Si trattava anche di costruire un momento di carattere scientifico con il quale esplorare aspetti disciplinari della questione che soprattutto nella loro applicazione presentano alcuni aspetti da valutare. L’occasione è stata suggerita dalla pubblicazione della special issue di Scienze Regionali – Italian Journal of Regional Science, dedicato a “diritti edificatori e governo del territorio: Verso una perequazione estesa” (vol. 13, n. 2/2014) curato da Roberto Camagni, Ezio Micelli e Stefano Moroni