On the Displacement Transmissibility of a Base Excited Viscously Damped Nonlinear Vibration Isolator

A vibration isolation system with a spring and a viscous damper subjected to base excitation

Regions in which the relative transmissibility has an infinite value (I), a finite maximum value (II) and does not have a maximum value (III) as a function of the nondimensional stiffness ratio γ and the nondimensional linear damping ratio ζ1; points A, B, C, and L correspond to the system parameters, which yield the relative and absolute transmissibilities shown in Figs.  3, 3; point D corresponds to (γ,ζ1)=(0,2/2) when the transmissibility curve loses its extremum

(a) Relative transmissibility curves for the points A, B, C, and L from Fig. 2 (for ζ2=0: A: ζ1=0.2 and γ=0.3 (red solid line); B: ζ1=0.2 and γ=−0.3 (blue dashed line); C: ζ1=0.8 and γ=0.3 (black (-..-) line); L: ζ1=0.2 and γ=0 (green dashed-dotted line)). (b) Absolute transmissibility curves for the points A, B, C, and L; dotted lines depict unstable solutions. (c) Regions (shaded) in which there is a multivalued response for ζ1=0.2 and a horizontal asymptote γa=(16/3)ζ12.

Regions (shaded) in which there is a multivalued response and a horizontal asymptote γa=(16/3)ζ12 for different values of the linear damping ratio: (a) ζ1=0.05, (b) ζ1=0.15, (c) ζ1=0.3, (d) ζ1=0.4

Regions (shaded) in which there is a multivalued response: (a) in the ζ1-γ plane with γc1 and γc2 defined by Eq. 18; and (b) in the ζ1-Ω plane with Ωc1 and Ωc2 defined by Eq. 17

The displacement transmissibility for a system with pure cubic viscous damping for different values of the nonlinear damping ratio: ζ2=0.01 (red solid line), ζ2=0.1 (blue dashed line), ζ2=0.2 (green dashed-dotted line) and ζ2=0.5 (black dotted line); (a) relative transmissibility and (b) absolute transmissibility. (For interpretation of the references to the color in this text, the reader is referred to the web version of this article).

Difference between the absolute transmissibilities of a linear system and a system with cubic damping T̃a for the same values of the damping ratio: ζ1=ζ2=0.1 (blue dashed line), ζ1=ζ2=0.2 (green dashed-dotted line), ζ1=ζ2=0.79 (red solid line) and ζ1=ζ2=1.5 (black dotted line)