A New Method of Generation of Nonlinear Normal Modes for Nonlinear Dynamics of Disordered Structures

Abstract eng:
Structural response can be affected by randomness under two different points of view – either in the forcing process and/or in the structural behaviour. Various approaches can be employed to investi-gate the structural response, among which polynomial chaos (Ghanem, Spanos [1]) and perturbation approaches (Liu et al. [2], Chiostrini and Facchini [3]) can be found. Both kinds of approaches require the investigation of the response variation in dependence on the (random) structural parameters, thus – often dramatically – increasing the number of degrees of freedom of the examined system. In case of linearity of the system response, a modal reduction approach can be effectively employed together with perturbation techniques; on the other hand, for some kind of nonlinear systems, such reduction approach (Bucher [4], Geschwindner [5]) might fail to give satisfactory results unless a very large number of modes is employed in the analysis (Betti et al. [6]). The task of reducing the number of degrees of freedom of nonlinear systems has therefore to be accomplished by means of alternative procedures, such as the introduction of nonlinear normal modes.

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