1. Date of download: 5/28/2016 Copyright © ASME. All rights reserved. From: Analysis and Experimental Estimation of Nonlinear Dispersion in a Periodic String J. Vib. Acoust. 2014;136(3):031016-031016-8. doi:10.1115/1.4027137 Nonlinear spring mass chain with cubic nonlinear interaction (δ denotes the relative displacement of neighboring masses) Figure Legend:

2. Date of download: 5/28/2016 Copyright © ASME. All rights reserved. From: Analysis and Experimental Estimation of Nonlinear Dispersion in a Periodic String J. Vib. Acoust. 2014;136(3):031016-031016-8. doi:10.1115/1.4027137 Amplitude-dependent dispersion in the monoatomic chain is strongly related to the Duffing backbone curve; when the wavenumber is π/3 the two are equal. Figure Legend:

3. Date of download: 5/28/2016 Copyright © ASME. All rights reserved. From: Analysis and Experimental Estimation of Nonlinear Dispersion in a Periodic String J. Vib. Acoust. 2014;136(3):031016-031016-8. doi:10.1115/1.4027137 Detail of bead and wire (a) and periodic string fixed to two upright aluminum I-beams (b) Figure Legend:

4. Date of download: 5/28/2016 Copyright © ASME. All rights reserved. From: Analysis and Experimental Estimation of Nonlinear Dispersion in a Periodic String J. Vib. Acoust. 2014;136(3):031016-031016-8. doi:10.1115/1.4027137 Test article and measurement hardware configuration Figure Legend:

5. Date of download: 5/28/2016 Copyright © ASME. All rights reserved. From: Analysis and Experimental Estimation of Nonlinear Dispersion in a Periodic String J. Vib. Acoust. 2014;136(3):031016-031016-8. doi:10.1115/1.4027137 FRF corresponding to the velocity response of bead 14 Figure Legend:

6. Date of download: 5/28/2016 Copyright © ASME. All rights reserved. From: Analysis and Experimental Estimation of Nonlinear Dispersion in a Periodic String J. Vib. Acoust. 2014;136(3):031016-031016-8. doi:10.1115/1.4027137 Snapshots of the forced dynamic deflection shapes (black circles) and theoretical deflection shapes (gray squares) near the resonant frequencies (labeled 1–14) and near the defect frequency (labeled accordingly). The 16 black markers indicate LDV measurement points that include the 14 beads and the two end points. The gray markers indicate theoretical deflection shapes expected for the theoretical model provided in Eq. (5). Note that no theoretical defect mode is plotted. Figure Legend:

7. Date of download: 5/28/2016 Copyright © ASME. All rights reserved. From: Analysis and Experimental Estimation of Nonlinear Dispersion in a Periodic String J. Vib. Acoust. 2014;136(3):031016-031016-8. doi:10.1115/1.4027137 The analytical model accurately captures the expected Bloch-wave dispersion, revealing a band gap in the neighborhood of 250 Hz. Markers correspond to the experimentally measured natural frequencies of the system (pictured on the right subfigure). Dashed and solid lines indicate dispersion relationships for periodic string and wire models, respectively. The inclusion of bending stiffness (wire model) improves the fit at higher frequencies. Figure Legend:

8. Date of download: 5/28/2016 Copyright © ASME. All rights reserved. From: Analysis and Experimental Estimation of Nonlinear Dispersion in a Periodic String J. Vib. Acoust. 2014;136(3):031016-031016-8. doi:10.1115/1.4027137 Sine sweep response recorded at the seventh bead is representative of the transition through resonance and jump phenomena typical of a Duffing-like system. The right subfigure reveals an essentially monochromatic response near the peak response. Figure Legend:

9. Date of download: 5/28/2016 Copyright © ASME. All rights reserved. From: Analysis and Experimental Estimation of Nonlinear Dispersion in a Periodic String J. Vib. Acoust. 2014;136(3):031016-031016-8. doi:10.1115/1.4027137 STFT spectrogram showing higher harmonic generation and the jump response occurring during sweep through resonance Figure Legend:

10. Date of download: 5/28/2016 Copyright © ASME. All rights reserved. From: Analysis and Experimental Estimation of Nonlinear Dispersion in a Periodic String J. Vib. Acoust. 2014;136(3):031016-031016-8. doi:10.1115/1.4027137 Several frequency up-sweeps performed from low (400 mVpp) to high (5 Vpp) excitation levels Figure Legend:

11. Date of download: 5/28/2016 Copyright © ASME. All rights reserved. From: Analysis and Experimental Estimation of Nonlinear Dispersion in a Periodic String J. Vib. Acoust. 2014;136(3):031016-031016-8. doi:10.1115/1.4027137 Jump phenomena and associated backbone curve Figure Legend:

12. Date of download: 5/28/2016 Copyright © ASME. All rights reserved. From: Analysis and Experimental Estimation of Nonlinear Dispersion in a Periodic String J. Vib. Acoust. 2014;136(3):031016-031016-8. doi:10.1115/1.4027137 Experimental dispersion shift and analytical dispersion diagram. The left subfigure depicts the typical Brillouin diagram with an additional third axis denoting amplitude (shift not to scale on left subfigure). The right subfigure depicts a zoom of the experimental backbone curve AB (black) and theoretical backbone curve for a simplified model (gray). Figure Legend: