Most engineering structures include nonlinearity to some degree. Depending on the dynamic conditions and level of external forcing, sometimes a linear structure assumption may be justified. However, design requirements of sophisticated structures such as satellites, stabilized weapon systems and radars may require nonlinear behavior to be considered for better performance. Therefore, it is very important to successfully detect, localize and parametrically identify nonlinearity in such cases. In engineering applications, the location of nonlinearity and its type may not be always known in advance. Furthermore, as the structure will be excited from only a few coordinates, the frequency response function matrices will not be complete. In order to parametrically identify more than one type of nonlinearity which may co-exist at the same location with the above mentioned limitations, a method is proposed where restoring force surface plots are used which are evaluated by describing function inversion. Then, by reformulating this method, a second method is proposed which can directly evaluate the total describing function of more than one type of nonlinearity which may co-exist at the same location without using any linear frequency response function matrix. It is also aimed in this study to use the nonlinearity localization formulations for damage localization purposes. The validation of the methods developed in this study is demonstrated with case studies based on simulated experiments, as well as real experiments with nonlinear structures and it is concluded that the methods are very promising to be used in engineering structures.

Damage and condition identi&amp / #64257 / cation of existing structures using non-destructive tests is a common challenge that has been worked on for a long time. In this study, two di&amp / #64256 / erent methods were developed to &amp / #64257 / nd existing force on cables as well as determine bending characteristics (EI coe&amp / #64259 / cients) of beam like structures (such as bridges). Comparing forces in symmetrically placed cables or against values obtained from design drawings would indicate structural imbalance as well as &amp / #64257 / nding EI coe&amp / #64259 / cients at a number of segments on a bridge girder might indicate weak regions that might possibly have undergone structural damage, having weak connections, lost composite action etc. With the help of the proposed algorithm, the sti&amp / #64256 / ness parameters of bridges can be assessed and the location of any damage that is in the magnitude which can a&amp / #64256 / ect displacement behavior of system can be located. The developed methods are demonstrated using the values analytically obtained from the created models and the e&amp / #64256 / ectiveness of the algorithm is criticized. Furthermore, several damage scenarios on a scaled lab beam was used to test the application using real experimental data / including tests on undamaged beam (for identi&amp / #64257 / cation) and tests on the damaged beam. Additional experiments were conducted on a cable stretched in the laboratory instrumented using a load cell to measure instantaneous axial load on the cable and compare these values against the values obtained from the developed tension measurement device. The results are compared and conclusions are derived.

Dans le domaine de l'ingénierie, connaitre le chargement appliqué sur une structure permet de résoudre des problèmes directs dont le résultat est le champ de déplacement, de déformation dans une structure. Il est alors possible d'effectuer un dimensionnement. Cependant, parfois ce chargement doit être identifie a posteriori. Malheureusement, il n'est pas toujours possible de mesurer ce chargement : ainsi, par exemple, on ne sait pas a priori où aura lieu le chargement, ou bien il n'est pas possible de placer un capteur sans l'endommager ou encore il peut nécessiter un encombrement trop important. On a alors recours à des mesures indirectes de déplacement, de déformation, d'accélération et on est alors amené à résoudre des problèmes inverses, qui sont en général mal posés. Il est alors nécessaire d'ajouter une (des) conditions supplémentaire(s) pour obtenir une solution unique et stable : c'est la régularisation du problème. Ces techniques sont bien connues et leur essor est dû à l'utilisation des décompositions en valeurs singulières des matrices de transfert. Toutefois, elles nécessitent l'utilisation d'un paramètre additionnel qui pondère cette condition supplémentaire : la détermination de ce paramètre est délicate. Peu de travaux ayant été réalisé pour tester de façon intensive les méthodes usuelles de régularisation (Tikhonov et troncature de la (G)SVD), en association avec les différents critères de détermination du paramètre de régularisation et les différentes réponses possibles, on a effectué un tel travail pour tirer des conclusions sur la méthodologie optimale. On a pu mettre en évidence que la mesure de l'accélération associée à un critère faisant intervenir les dérivées du signal à reconstruire donne en général les meilleurs résultats sous réserve d'utiliser le critère GCV pour déterminer le paramètre de régularisation. Ces méthodes supposent que la localisation de la zone de chargement est connue. Aussi on s'est intéressé à déduire cette zone de chargement en tentant de reconstruire des chargements identiquement nuls. Cette identification a été effectuée aisément sous réserve qu'on ait peu de forces à identifier par rapport au nombre de mesures disponibles. En revanche une telle identification est délicate lorsqu'on n'a pas plus de mesures que de forces à identifier. Finalement on s'est tourné vers l'identification de chargement ayant plastifié la structure étudiée. On a alors essayé de reconstruire le chargement en supposant que la structure reste linéaire élastique, alors qu'elle a été plastifiée : on a utilisé la méthode du double chargement et effectue des simulations à l'aide du logiciel de simulation Ls-dyna.La force reconstruite fait alors apparaitre une composante statique traduisant la déformation résiduelle dans la structure. Dans ce cas, la réponse à utiliser pour identifier le chargement est une déformation dans une zone non plastifiée / In the field of the engineering, knowing the load applied on the structure which allows to solve the direct problem of which the results are given the field of displacement and strain in a structure. It is possible to perform a dimensioning. However, sometimes this load must be identified a posteriori. Unfortunately, it is not always possible to measure this load. Thus, for example, we do not know a priori where it will be loaded, either it is not possible to place a sensor without damaging it or needs too much space. We then have to use indirect measures of displacement, strain, acceleration and then we are lead to solve the inverse problems which are generally an ill-posed. It is then necessary to add one (or more) conditions to obtain a unique and stable solution: it is the regularization of the problem. These techniques are well known and their development is due to the use of the singular value decomposition of the transfer matrix. However, they require the use of an additional parameter that weights this additional condition: the determination of this parameter is difficult. Few studies having been realized in way the usual regularization methods of (Tikhonov and truncation of the (G)SVD), in association with the various criteria for determining the regularization parameter and the various possible responses, we conducted a such work, to draw conclusions on the optimal methodology. It has been highlighted that the measurement of the acceleration associated with a criterion involving the derived signal to reconstruct generally gives the best results via the GCV criterion to determine the regularization parameter. These methods suppose that the location of the loading area is known. We also were interested to deduct this loading area while trying to reconstruct load that is identically zero. This identification was performed easily that has little load to identify compared to the number of measurements available. However such identification is difficult when there are no more measures than loads to identify. Finally we turned to the identification of loading with the plastic structure. We then tried to reconstruct the load assuming that the structure remains linear-elastic, while it was plasticized: we used the method of the double load and performed simulations using the software ls-dyna. The reconstructed load then shows a static component reflecting the residual strain in the structure. In this case, the response used to identify the load is a strain in a non-plasticized zone