Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Superharmonic Resonance of Order 2 for an Impacting Hertzian Contact Oscillator: Theory and Experiments J. Comput. Nonlinear Dynam. 2006;2(2):190-196. doi:10.1115/1.2447549 Figure Legend: Dynamic model of the SDOF impact oscillator

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Superharmonic Resonance of Order 2 for an Impacting Hertzian Contact Oscillator: Theory and Experiments J. Comput. Nonlinear Dynam. 2006;2(2):190-196. doi:10.1115/1.2447549 Figure Legend: The experimental test rig

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Superharmonic Resonance of Order 2 for an Impacting Hertzian Contact Oscillator: Theory and Experiments J. Comput. Nonlinear Dynam. 2006;2(2):190-196. doi:10.1115/1.2447549 Figure Legend: Magnitudes of the two first harmonic components H1 and H2 of the transmitted force versus the dimensionless excitation frequency. Theoretical results obtained by the shooting method (σ=24.5%): stable responses (thick line); unstable responses (thin line); experimental results (σ=28.5%) (square).

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Superharmonic Resonance of Order 2 for an Impacting Hertzian Contact Oscillator: Theory and Experiments J. Comput. Nonlinear Dynam. 2006;2(2):190-196. doi:10.1115/1.2447549 Figure Legend: Phases of the two first harmonic components H1 and H2 of the transmitted force versus the dimensionless excitation frequency. Theoretical results obtained by the shooting method (σ=24.5%): stable responses (thick line); unstable responses: (thin line); experimental results (σ=28.5%) (square).

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Superharmonic Resonance of Order 2 for an Impacting Hertzian Contact Oscillator: Theory and Experiments J. Comput. Nonlinear Dynam. 2006;2(2):190-196. doi:10.1115/1.2447549 Figure Legend: Frequency response curve of the magnitude A defined by Eq. . Multiple scales method (σ=25.5%) (thick line); shooting method (σ=24.5%) (thin line).

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Superharmonic Resonance of Order 2 for an Impacting Hertzian Contact Oscillator: Theory and Experiments J. Comput. Nonlinear Dynam. 2006;2(2):190-196. doi:10.1115/1.2447549 Figure Legend: Frequency response curve of the phase φ defined by Eq. . Multiple scales method (σ=25.5%) (thick line); shooting method (σ=24.5%) (thin line).

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Superharmonic Resonance of Order 2 for an Impacting Hertzian Contact Oscillator: Theory and Experiments J. Comput. Nonlinear Dynam. 2006;2(2):190-196. doi:10.1115/1.2447549 Figure Legend: Magnitudes of the two first harmonic components H1 and H2 of the transmitted force versus the dimensionless excitation frequency. Theoretical results obtained by the shooting method (σ=26.5%): stable responses (thick line); unstable responses (thin line); experimental results (σ=29.5%) (square).

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Superharmonic Resonance of Order 2 for an Impacting Hertzian Contact Oscillator: Theory and Experiments J. Comput. Nonlinear Dynam. 2006;2(2):190-196. doi:10.1115/1.2447549 Figure Legend: Phases of the two first harmonic components H1 and H2 of the transmitted force versus the dimensionless excitation frequency. Theoretical results obtained by the shooting method (σ=26.5%): stable responses (thick line); unstable responses (thin line); experimental results (σ=29.5%) (square).

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Superharmonic Resonance of Order 2 for an Impacting Hertzian Contact Oscillator: Theory and Experiments J. Comput. Nonlinear Dynam. 2006;2(2):190-196. doi:10.1115/1.2447549 Figure Legend: Magnitudes of the second harmonic component H2 of the transmitted force versus the dimensionless excitation frequency. Theoretical results obtained by the shooting method (σ=25%): stable responses (thick line); unstable responses (thin line).

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Superharmonic Resonance of Order 2 for an Impacting Hertzian Contact Oscillator: Theory and Experiments J. Comput. Nonlinear Dynam. 2006;2(2):190-196. doi:10.1115/1.2447549 Figure Legend: Phases of the second harmonic components H2 of the transmitted force versus the dimensionless excitation frequency. Theoretical results obtained by the shooting method (σ=25%): stable responses (thick line); unstable responses (thin line).

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Superharmonic Resonance of Order 2 for an Impacting Hertzian Contact Oscillator: Theory and Experiments J. Comput. Nonlinear Dynam. 2006;2(2):190-196. doi:10.1115/1.2447549 Figure Legend: The various regions in parameter space (ϖ,σ) for the existence of the steady state responses (TB) indicates transcritical bifurcation

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Superharmonic Resonance of Order 2 for an Impacting Hertzian Contact Oscillator: Theory and Experiments J. Comput. Nonlinear Dynam. 2006;2(2):190-196. doi:10.1115/1.2447549 Figure Legend: Time history of the dimensionless nonlinear elastic force transmitted through the contact at ϖ=0.484: (a) experimental result (σ=28.5%); and (b) theoretical result (σ=24.5%) obtained by the central difference method. Dashed line indicates zero force.

Date of download: 10/21/2017 Copyright © ASME. All rights reserved. From: Superharmonic Resonance of Order 2 for an Impacting Hertzian Contact Oscillator: Theory and Experiments J. Comput. Nonlinear Dynam. 2006;2(2):190-196. doi:10.1115/1.2447549 Figure Legend: Time history of the dimensionless nonlinear elastic force transmitted through the contact at ϖ=0.463: (a) experimental result (σ=29.5%); (b) theoretical result (σ=26.5%) obtained by the central difference method. Dashed line indicates zero force.