Modeling and experimental identification of vibrating structures: localized and distributed nonlinearities

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Free-Decay Nonlinear System Identification via Mass-Change Scheme

Methods for nonlinear system identification of structures generally require input-output measured data to estimate the nonlinear model, as a consequence of the noninvariance of the FRFs in nonlinear systems. However, providing a continuous forcing input to the structure may be difficult or impracticable in some situations, while it may be much easier to only measure the output. This paper deals with the identification of nonlinear mechanical vibrations using output-only free-decay data. The presented method is based on the nonlinear subspace identification (NSI) technique combined with a mass-change scheme, in order to extract both the nonlinear state-space model and the underlying linear system. The technique is tested first on a numerical nonlinear system and subsequently on experimental measurements of a multi-degree-of-freedom system comprising a localized nonlinearity

Experimental Characterization of Friction in a Negative Stiffness Nonlinear Oscillator

Nonlinear dissipative phenomena are common features of many dynamical systems and engineering applications, and their experimental characterization has always been a challenge among the research community. Within the wide range of nonlinear damping mechanisms, friction is surely one of the most common, and with a high impact on the dynamical behavior of structures. In this paper, the nonlinear identification of friction in a negative stiffness oscillator is pursued. The structure exhibits a strong nonlinear behavior, mainly due to its polynomial elastic restoring force with a negative stiffness region. This leads to an asymmetric double-well potential with two stable equilibrium positions, and the possibility of switching between them in a chaotic way. Friction plays a crucial role in this context, as it derives from the continuous sliding between the central guide and the moving mass. The system is driven through harmonic tests with several input amplitudes, in order to estimate the variations in the energy dissipated per cycle. The identification of the frictional behavior is then pursed by minimizing the errors between the experimental measurements and the model predictions, using the harmonic balance method in conjunction with a continuation technique on the forcing amplitudes

Nonlinear dynamics of a negative stiffness oscillator: experimental identification and model updating

Systems exhibiting a negative stiffness region are often used as vibration isolators, due to their enhanced damping properties. The device tested in this paper is part of a damping system and it acts like an asymmetric double-well Duffing oscillator, with two stable and one unstable equilibrium positions. The range of motion can either be bounded around one stable position (in-well oscillations) or include all the three positions (cross-well oscillations). Depending on the input amplitude, the oscillator can exhibit linear and nonlinear dynamics, and chaotic motion as well. Due to its asymmetrical design, the two linearized systems associated to small-amplitude oscillations around one stable equilibrium position are different. In this work, the dynamical behavior of the system is first investigated in the case of linear and nonlinear in-well oscillations and then in the case of cross-well oscillations with chaotic motion. To accomplish this task, the device is mounted on a shaking table and it is driven through several excitation levels with both harmonic and random inputs. An experimental bifurcation tracking analysis is also carried out to understand the possible response scenarios. Afterwards, the nonlinear identification is performed using nonlinear subspace algorithms to extract the restoring force of the system. Eventually, the physically-based model of the device is updated to match the identified characteristics via genetic algorithms

Experimental characterization of a nonlinear mechanical oscillator with softening behaviour for large displacements

This paper presents an experimental insight into the performance of a mechanical oscillator consisting of an X-shaped-spring configuration. This configuration achieves an overall softening characteristic with quasi-zero stiffness behaviour far away from the static equilibrium point. Such a geometrical nonlinear configuration has attracted significant research attention in the last few years, particularly for its application as a vibration isolator with the possibility to extend the quasi-zero-stiffness region beyond that of the classical three-spring nonlinear isolator. However, previous experimental evidence has been limited to small amplitude vibration excitation only. Furthermore, it has been focused mainly on the isolation region, rather than on the large amplitude response, thus circumventing an insight on the damping effects and its modelling. To address this gap, in this paper, both frequency sweeps and random excitations are applied to a prototype device for experimental characterization. A nonlinear stiffness model is developed based on the geometry of the system and a nonlinear damping model is assumed based on experimental observation. The proposed model accurately describes the dynamic behaviour of the system as shown by comparison of theoretical and experimental data

Identification of Nonlinear Damping Using Nonlinear Subspace Method

In this paper, the identification problem is discussed for damping nonlinearity. In practical applications, nonlinear damping is widespread, which is inevitable in the vibration response. Within the wide range of nonlinear damping mechanisms, friction is surely one of the most common, and with a high impact on the dynamical behavior of structures. Two common kinds of friction are investigated: quadratic friction and Coulomb friction. Nonlinear damping parameters are identified by nonlinear subspace identification, where the damping nonlinearity of the system is considered as a feedback force applied to the underlying linear system and is identified utilizing the time domain data. Two simulation examples are conducted to verify the effectiveness of the method. Results confirm the effectiveness of the methodology in identifying damping nonlinearities

Automatic Nonlinear Subspace Identification Using Clustering Judgment Based on Similarity Filtering

Accurately determining system order plays a vital role in system identification directly related to the accuracy of identification results, especially for nonlinear system identification. Due to the need for human subjective judgment, the traditional sequence determination method easily causes uncertainty in the results; and the phenomenon of the virtual mode or omission occurs. An automatic nonlinear subspace identification method is proposed to address the aforementioned problems. When the eigenvalue decomposition of the constructed Hankel matrix is performed, the calculation range of the modal order of the system is estimated. The similarity coefficient and distance function are introduced to cluster the identified modal results, the poles of the false modes are removed to obtain the cluster stabilization diagram, and the best order of the system is received. Then, the modal parameters and nonlinear coefficients are obtained. Simulation examples are carried out to verify the effectiveness and robustness of the proposed method. An experimental study is carried out on a multilayer building with nonlinear characteristics. Compared with the traditional stabilization graph, the accuracy of the automatic order determination proposed in this paper is proven

REGIONAL MAPPING OF MYOCARDIAL HIBERNATION PHENOTYPE IN IDIOPATHIC END-STAGE DILATED CARDIOMYOPATHY

Myocardial hibernation (MH) is a well-known feature of human ischaemic cardiomyopathy (ICM), whereas its presence in human idiopathic dilated cardiomyopathy (DCM) is still controversial. We investigated the histological and molecular features of MH in left ventricle (LV) regions of failing DCM or ICM hearts. We examined failing hearts from DCM (n = 11; 41.9 ± 5.45 years; left ventricle-ejection fraction (LV-EF), 18 ± 3.16%) and ICM patients (n = 12; 58.08 ± 1.7 years; LVEF, 21.5 ± 6.08%) undergoing cardiac transplantation, and normal donor hearts (N, n = 8). LV inter-ventricular septum (IVS) and antero-lateral free wall (FW) were transmurally (i.e. sub-epicardial, mesocardial and sub-endocardial layers) analysed. LV glycogen content was shown to be increased in both DCM and ICM as compared with N hearts (P < 0.001), with a U-shaped transmural distribution (lower values in mesocardium). Capillary density was homogenously reduced in both DCM and ICM as compared with N (P < 0.05 versus N), with a lower decrease independent of the extent of fibrosis in sub-endocardial and sub-epicardial layers of DCM as compared with ICM. HIF1-α and nestin, recognized ischaemic molecular hallmarks, were similarly expressed in DCM-LV and ICM-LV myocardium. The proteomic profile was overlapping by ~50% in DCM and ICM groups. Morphological and molecular features of MH were detected in end-stage ICM as well as in end-stage DCM LV, despite epicardial coronary artery patency and lower fibrosis in DCM hearts. Unravelling the presence of MH in the absence of coronary stenosis may be helpful to design a novel approach in the clinical management of DCM

A study on the optimal spatial damping distribution in railway pantograph-catenary interaction

Railway overhead contact lines are very low-damped structures with a high modal density in the low-frequency region. This has a significant impact on the interaction with the pantograph, especially in the high-speed case and in multiple pantographs operations. This paper studies the optimal spatial damping distribution in overhead contact lines obtained by introducing localised damping connections, resulting in a non-proportional damping distribution. To this end, the simulation software Cateway is presented and adopted in conjunction with evolutionary multi-objective optimisers to seek for the most efficient spatial damping distribution. The study is conducted on a high-speed reference model considering two different train speeds. The final goal of this optimisation is to obtain useful hints about the most and least sensitive regions to damping modifications. A dedicated study on the locus of the poles of the system is also proposed to corroborate the findings of the analysis. Results show that significant improvements on the current collection quality can be achieved by carefully designing the spatial damping distribution, especially for the rear (trailing) pantograph. On the other hand, wrong design choices can lead to a degradation of the contact forces