Date of download: 10/10/2017 Copyright © ASME. All rights reserved. From: On the Performance of a Two-Stage Vibration Isolation System Which has Geometrically Nonlinear Stiffness J. Vib. Acoust. 2014;136(6):064501-064501-5. doi:10.1115/1.4028379 Figure Legend: Comparison of the transmissibility of a single-stage linear isolator and a two-stage linear isolator as a function of nondimensional frequency. The mass ratio is 0.2, the upper stiffness is equal to the lower stiffness, and the damping ratio for the upper and lower stages is 0.01. Single-stage linear isolator, red solid line; two-stage linear isolator, blue dashed line.

Date of download: 10/10/2017 Copyright © ASME. All rights reserved. From: On the Performance of a Two-Stage Vibration Isolation System Which has Geometrically Nonlinear Stiffness J. Vib. Acoust. 2014;136(6):064501-064501-5. doi:10.1115/1.4028379 Figure Legend: Schematic of the two-stage nonlinear isolation system. (a) Actual system and (b) equivalent lumped parameter model. The mass m1 is the suspended (primary) mass and m2 is the intermediate (secondary) mass.

Date of download: 10/10/2017 Copyright © ASME. All rights reserved. From: On the Performance of a Two-Stage Vibration Isolation System Which has Geometrically Nonlinear Stiffness J. Vib. Acoust. 2014;136(6):064501-064501-5. doi:10.1115/1.4028379 Figure Legend: Illustration of the HBM and numerical solution for force and displacement transmissibility when the upper and lower horizontal stiffness are fixed at k∧h1 = k∧h2 = 1.17 and l∧ = 0.7, F∧e = F∧emax, X∧e = X∧emax, μ = 0.2, k∧v2 = 1, and ζ1 = ζ2 = 0.01. HBM solution: force transmissibility (blue solid line), displacement transmissibility (red dashed line). Numerical solution obtained by direct numerical integration of Eqs. (2) and (8) (decreasing frequency: black and green “+”; increasing frequency: black and green “o”).

Date of download: 10/10/2017 Copyright © ASME. All rights reserved. From: On the Performance of a Two-Stage Vibration Isolation System Which has Geometrically Nonlinear Stiffness J. Vib. Acoust. 2014;136(6):064501-064501-5. doi:10.1115/1.4028379 Figure Legend: Plots of force and displacement transmissibilities of the two-stage nonlinear isolator with the same parameters as in Fig. 3, showing the effects of changing the horizontal stiffness, k∧h1 and k∧h2. (a) and (b) Force transmissibility, (c) and (d) displacement transmissibility: (a) and (c), Effects of setting k∧h1 = 0 and adjusting k∧h2: red dashed line, k∧h2 = 0; black dashed–dotted line, k∧h2 = 0.7; green dotted line, k∧h2 = 1; blue solid line, k∧h2 = 1.17; (b) and (d), Effect of fixing k∧h2 = 1.17 and adjusting k∧h1: blue solid line, k∧h1 = 0; green dotted line, k∧h1 = 0.7; black dashed–dotted line, k∧h1 = 1; red dashed line, k∧h1 = 1.17.