Analysis of a non-linear structure by considering two non-linear formulations |
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Authors: | R Majed |
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Institution: | a Institut Préparatoire aux Etudes d’Ingénieurs de Nabeul, IPEIN Campus Universitaire Merazka, 8000 Nabeul, Tunisiab Laboratoire de Mécanique Appliquée R. Chaleat, UMR CNRS-UFC 66 04, UFRST, Université de Franche-Comté, 24, Rue de l’Epitaphe, 25030 Besançon Cedex, France |
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Abstract: | In recent years, modal synthesis methods have been extended for solving non-linear dynamic problems subjected to harmonic excitation. These methods are based on the notion of non-linear or linearized modes and exploited in the case of structures affected by localized non-linearity. Actually, the experimental tests executed on non-linear structures are time consuming, particularly when repeated experimental tests are needed. It is often preferable to consider new non-linear methods with a view to decrease significantly the number of attempts during prototype tests and improving the accuracy of the dynamic behaviour.This article describes two fundamental non-linear formulations based on two different strategies. The first formulation exploits the eigensolutions of the associated linear system and the dynamics characteristics of each localized non-linearity. The second formulation is based on the exploitation of the linearized eigensolutions obtained using an iterative process. This article contains a numerical and an experimental study which examines the non-linear behaviour of the structure affected by localized non-linearities. The study is intended to validate the numerical algorithm and to evaluate the problems arising from the introduction of non-linearities. The complex responses are evaluated using the iterative Newton-Raphson method and for a series of discrete frequencies. The theory has been applied to a bi-dimensional structure and consists of evaluating the harmonic responses obtained using the proposed formulations by comparing measured and calculated transfer functions. |
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