1. Date of download: 9/26/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Transient Dynamics of Pendulum Torsional Vibration Absorbers—Part I: Theory
J. Vib. Acoust. 2013;135(1): doi: /
Figure Legend:
Depiction of the CPVA system model showing three possible paths for the absorber COM. The outermost (circular) and innermost (cycloidal) paths bound the two-parameter family under consideration; the middle path corresponds to the tautochrone. The paths are shown enlarged, and not to scale relative to the rotor, to exaggerate the differences in the paths.

2. Date of download: 9/26/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Transient Dynamics of Pendulum Torsional Vibration Absorbers—Part I: Theory
J. Vib. Acoust. 2013;135(1): doi: /
Figure Legend:
A damped zero initial condition transient trajectory, IC 1, obtained from simulations of the general path averaged equations, indicating the peak and steady-state amplitudes: (a) shown in the phase space, and (b) as the absorber response versus θ. System parameter values: Dc = 0.30 and χc = 0.10. Also shown in (a) is the trajectory from the unstable manifold of the saddle that tends toward the desired steady state.

3. Date of download: 9/26/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Transient Dynamics of Pendulum Torsional Vibration Absorbers—Part I: Theory
J. Vib. Acoust. 2013;135(1): doi: /
Figure Legend:
Simulations of the full EOM (Eqs. (1) and (2)) for ε = 0.03 and n = 1.5, and three sets of system parameter values that yield χc = 0.112, with a predicted overshoot of 122%. (a) Γc = 1.171, n˜ = 1.52 (σc = -4.263), λ = 0 (ξc = -4.22), simulated percent overshoot = 119%; (b) Γc = 0.799, n˜ = 1.51 (σc = -3.253), λ = 0.1 (ξc = -4.03), simulated percent overshoot = 121%; and (c) Γc = 0.477, n˜ = 1.5 (σc = -2.25), λ = 0.2 (ξc = -3.732), simulated percent overshoot = 124%. Additional parameters used to simulate the full EOM include: Γ0 = Γ/2, α = 0, and β = 1.

4. Date of download: 9/26/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Transient Dynamics of Pendulum Torsional Vibration Absorbers—Part I: Theory
J. Vib. Acoust. 2013;135(1): doi: /
Figure Legend:
The percent overshoot of an absorber system subject to zero initial conditions, computed using the pseudoenergy method for Di = 0, and using the averaged equations for Di≠0; for (a) general path and (b) near-tautochronic path absorbers

5. Date of download: 9/26/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Transient Dynamics of Pendulum Torsional Vibration Absorbers—Part I: Theory
J. Vib. Acoust. 2013;135(1): doi: /
Figure Legend:
The rotor and absorber response to a step input of sinusoidal torque. (a) Rotor and (b) absorber response to input +Γsin(nθ), resulting in absorber overshoot of %; (c) rotor and (d) absorber response to input -Γsin(nθ), resulting in absorber overshoot of %. Simulation data: ε = 0.07, Γc = 0.71, n˜ = 1.51, λ = 0, ζ = 0.002, Γ0 = Γ/2, α = 0, and β = 1. For these parameters, χc = 0.161, Dc = 0.10, and the pseudoenergy theory predicts absorber overshoot of %.

6. Date of download: 9/26/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Transient Dynamics of Pendulum Torsional Vibration Absorbers—Part I: Theory
J. Vib. Acoust. 2013;135(1): doi: /
Figure Legend:
Comparison of the general path pseudoenergy method with simulations of the full EOM for μ = 0, n = 1.5, ε = 0.03, Γ0 = Γ/2, α = 0, and β = 1. Solid line is the pseudoenergy prediction. Simulation data: sweep of χc by varying λ from 0.80 to 0 with εΓ = 0.005, and σc = -3.25 (n˜ = 1.51). Sweep of χc by varying εΓ from to with ξc = -4.09(λ = 0), and σc = -3.25 (n˜ = 1.51). Sweep of χc by varying n˜ from 1.58 to with εΓ = 0.003 (note that in this case varying n˜ results in sweeping ξc from − 5 to −4 for a fixed λ = 0).

7. Date of download: 9/26/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Transient Dynamics of Pendulum Torsional Vibration Absorbers—Part I: Theory
J. Vib. Acoust. 2013;135(1): doi: /
Figure Legend:
Comparison of the general path pseudoenergy method with simulations of the full EOM for μ = 0, n = 1.5, Γ0 = Γ/2, α = 0, and β = 1. Solid line is the pseudoenergy prediction. (a) ε = 0.07 with simulation data: sweep of χc by varying λ from 0.80 to 0 with εΓ = 0.012, and σc = -2.68 (n˜ = 1.51). Sweep of χc by varying εΓ from to with ξc = -4.09 (λ = 0), and σc = -2.68 (n˜ = 1.51). Sweep of χc by varying n˜ from 1.58 to with εΓ = 0.01 (note that in this case varying n˜ results in varying ξc from −5 to −4 for a fixed λ = 0) (b) ε = 0.10 with simulation data: sweep of χc by varying λ from 0.80 to 0 with εΓ = 0.019, and σc = -2.55 (n˜ = 1.51). Sweep of χc by varying εΓ from to with ξc = -4.09 (λ = 0), and σc = -2.55 (n˜ = 1.51). Sweep of χc by varying n˜ from 1.58 to with εΓ = 0.016 (note that in this case varying n˜ results in sweeping ξc from −5 to −4 for a fixed λ = 0).

8. Date of download: 9/26/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Transient Dynamics of Pendulum Torsional Vibration Absorbers—Part I: Theory
J. Vib. Acoust. 2013;135(1): doi: /
Figure Legend:
Comparison of the general path pseudoenergy method with simulations of the full EOM for Dc = 0.05 (ζ = 0.001) and Dc = 0.10 (ζ = 0.002). Simulation data: sweep of χc by varying λ from 0 to 0.80 with εΓ =  Sweep of χc by varying εΓ from to with ξc = -4.09 (λ = 0). Other parameter values used in simulations are: n˜ = 1.51, n = 1.5, ε = 0.07, Γ0 = Γ/2, α = 0, and β = 1.

9. Date of download: 9/26/2017
Copyright © ASME. All rights reserved.
From: Nonlinear Transient Dynamics of Pendulum Torsional Vibration Absorbers—Part I: Theory
J. Vib. Acoust. 2013;135(1): doi: /
Figure Legend:
Comparison of the near-tautochronic path pseudoenergy method with simulations of the full EOM for λ = λe, μ = 0, n = 1.5, ε = 0.07, Γ0 = Γ/2, α = 0, and β = 1. (a) Simulation data: sweep of χt by varying εΓ from to and σt = -2.68 (n˜ = 1.51). (b) Simulation data: sweep of χt by varying n˜ from 1.67 to 1.50 with εΓ = 0.028.