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Technical Briefs

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

[+] Author and Article Information
Zarko Milovanovic

Department of Mechanics, Faculty of Technical Sciences, University of Novi Sad, Novi Sad 21000, Serbia

Ivana Kovacic

Department of Mechanics, Faculty of Technical Sciences, University of Novi Sad, Novi Sad 21000, Serbiaivanakov@uns.ac.rs

Michael J. Brennan

Institute of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, UKmjb@isvr.soton.ac.uk

J. Vib. Acoust 131(5), 054502 (Sep 11, 2009) (7 pages) doi:10.1115/1.3147140 History: Received October 17, 2008; Revised March 14, 2009; Published September 11, 2009

## Abstract

In this article vibration isolators having linear and cubic nonlinearities in stiffness and damping terms are considered under base excitation. The influence of the system parameters on the relative and absolute displacement transmissibility is investigated. The performance characteristics of the nonlinear isolators are evaluated and compared with the performance characteristics of the linear isolators to highlight the beneficial effects in the nonlinear systems considered.

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## Figures

Figure 1

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

Figure 2

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.  33; point D corresponds to (γ,ζ1)=(0,2/2) when the transmissibility curve loses its extremum

Figure 3

(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.

Figure 4

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

Figure 5

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

Figure 6

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).

Figure 7

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)

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