The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part I. One reason of the still limited use of NNMs in structural dynamics is that their computation is often regarded as impractical. However, when resorting to numerical algorithms, we show that the NNM computation is possible with limited implementation effort, which paves the way to a practical method for determining the NNMs of nonlinear mechanical systems. The proposed algorithm relies on two main techniques, namely a shooting procedure and a method for the continuation of NNM motions. The algorithm is demonstrated using four different mechanical systems, a weakly and a strongly nonlinear two-degree-of-freedom system, a simplified discrete model of a nonlinear bladed disk and a nonlinear cantilever beam discretized by the finite element method.

a b s t r a c tThis study addresses the mitigation of a nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA), is introduced in this paper. An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is tailored according to the nonlinear restoring force of the primary system. The NLTVA parameters are then determined using a nonlinear generalization of Den Hartog's equal-peak method. The mitigation of the resonant vibrations of a Duffing oscillator is considered to illustrate the proposed developments.

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This paper considers the RL shunt damping of rotationally periodic structures with an array of regularly spaced piezoelectric patches. The technique is targeted to the damping of a specific mode withnnodal diameters. For this particular case, one can take advantage of the shape of the targeted mode to organize the piezoelectric patches as a modal filter (in parallel loops) which reduces the demand on the inductors of the tuned inductive shunt. In the case of a perfectly rotationally periodic structure, it is possible to organize 4npiezoelectric transducers (PZT patches) in two parallel loops of 2npatches each. In this way, the demand on the inductors is reduced by4n2as compared to independent loops, which may allow a fully passive integration of the RL shunt in a turbomachinery application. The method is first illustrated experimentally on a circular plate; it is then applied to a prototype of an industrial bladed drum. The influence of blade mistuning is investigated.