Experimental study of isolas in nonlinear systems featuring modal interactions.

The objective of the present paper is to provide experimental evidence of isolated resonances in the frequency response of nonlinear mechanical systems. More specifically, this work explores the presence of isolas, which are periodic solutions detached from the main frequency response, in the case of a nonlinear set-up consisting of two masses sliding on a horizontal guide. A careful experimental investigation of isolas is carried out using responses to swept-sine and stepped-sine excitations. The experimental findings are validated with advanced numerical simulations combining nonlinear modal analysis and bifurcation monitoring. In particular, the interactions between two nonlinear normal modes are shown to be responsible for the creation of the isolas.

Vibrational dynamics of vocal folds using nonlinear normal modes.

Many previous works involving physical models, excised and in vivo larynges have pointed out nonlinear vibration in vocal folds during voice production. Moreover, theoretical studies involving mechanical modeling of these folds have tried to gain a profound understanding of the observed nonlinear phenomena. In this context, the present work uses the nonlinear normal mode theory to investigate the nonlinear modal behavior of 16 subjects using a two-mass mechanical modeling of the vocal folds. The free response of the conservative system at different energy levels is considered to assess the impact of the structural nonlinearity of the vocal fold tissues. The results show very interesting and complex nonlinear phenomena including frequency-energy dependence, subharmonic regimes and, in some cases, modal interactions, entrainment and bifurcations.

Effective particles and classification of the dynamics of homogeneous granular chains with no precompression.

We develop a systematic methodology for classifying the periodic orbits of homogeneous ordered granular chains with no dissipation, under the assumption that all granules oscillate with the same frequency. The analysis is based on the idea of balancing linear momentum for sets of auxiliary models consisting of "effective particles." The auxiliary models may be defined for any given finite, ordered granular chain composed of n identical granules (beads) that interact with each other through strongly nonlinear Hertzian interaction law. In turn, the auxiliary models may be effectively used for theoretically predicting the total number of periodic orbits and the corresponding amplitude ratios of the granules. Good correspondence between the theoretical models and results of direct numerical simulations is reported. The results presented herein can be used to understand the complex intrinsic dynamics of ordered granular media, and to systematically study the generation of mode localization in these strongly nonlinear systems. The derived analytical models can be utilized to predict the response of the effective particles, and based on that, to predict primary pulse transmission in periodic layered media with granular interfaces. Moreover, our analysis can be extended to the general class of nonlinear chains of particles with smooth interacting potentials and possible separation between particles during the motion.