The University of Southampton
University of Southampton Institutional Repository

The effects of cubic damping on vibration isolation

The effects of cubic damping on vibration isolation
The effects of cubic damping on vibration isolation
Vibration isolators are often assumed to possess linear viscous damping which has well known consequences for their performance. However, damping may be designed to be or prove to be nonlinear. This study investigates the effect of cubic damping, as an example of damping nonlinearity, in a single degree of freedom (SDOF) vibration isolation system. The response behaviour due to two excitation types, namely harmonic and broadband excitations, was examined.

For harmonic excitation, the Harmonic Balance Method (HBM) was applied to yield approximate closed form solutions and simplified analytical expressions implicitly show the influence of cubic damping for particular frequency regions. The HBM solutions were verified using direct numerical integration. The presence of cubic damping proves to be beneficial for the force excited case. It reduces response amplitude around the resonance frequency and has similar response to an undamped system in the isolation region. In contrast, for base excitation, the cubic damping is detrimental at high excitation frequencies as the base excitation and isolated mass move almost together. The effect becomes more pronounced for larger excitation amplitudes.

The case of base excitation was then considered for broadband excitation. The responses using direct numerical integration were presented using power spectral densities. In contrast to harmonic excitation, the amplitude of the response does not appear to approach that of the input. Instead, a higher effective cubic damping results in a higher vibration level of the isolated mass at frequencies below the resonance frequency. It also does not reduce explicitly the response amplitude around the resonance frequency unlike the linear viscous damping. For a constant displacement amplitude random excitation, the excitation frequency bandwidth is found to be a significant factor in the level of effective cubic damping. A broader excitation bandwidth results in a higher level of cubic damping force.

The theoretical and numerical results for both harmonic and broadband excitation were validated experimentally. The experimental investigation was performed using a SDOF base excited vibration isolation system possessing a simple velocity feedback control active damper to reproduce the nonlinear damping force. The predictions were shown to be in good agreement with measurements thereby verifying the effects of cubic damping on a SDOF system undergoing harmonic and broadband base excitation.
Panananda, Nuttarut
e3dbe02e-c9d2-4354-870c-b399b16eb917
Panananda, Nuttarut
e3dbe02e-c9d2-4354-870c-b399b16eb917
Ferguson, Neil
8cb67e30-48e2-491c-9390-d444fa786ac8

Panananda, Nuttarut (2014) The effects of cubic damping on vibration isolation. University of Southampton, Faculty of Engineering and the Environment, Doctoral Thesis, 250pp.

Record type: Thesis (Doctoral)

Abstract

Vibration isolators are often assumed to possess linear viscous damping which has well known consequences for their performance. However, damping may be designed to be or prove to be nonlinear. This study investigates the effect of cubic damping, as an example of damping nonlinearity, in a single degree of freedom (SDOF) vibration isolation system. The response behaviour due to two excitation types, namely harmonic and broadband excitations, was examined.

For harmonic excitation, the Harmonic Balance Method (HBM) was applied to yield approximate closed form solutions and simplified analytical expressions implicitly show the influence of cubic damping for particular frequency regions. The HBM solutions were verified using direct numerical integration. The presence of cubic damping proves to be beneficial for the force excited case. It reduces response amplitude around the resonance frequency and has similar response to an undamped system in the isolation region. In contrast, for base excitation, the cubic damping is detrimental at high excitation frequencies as the base excitation and isolated mass move almost together. The effect becomes more pronounced for larger excitation amplitudes.

The case of base excitation was then considered for broadband excitation. The responses using direct numerical integration were presented using power spectral densities. In contrast to harmonic excitation, the amplitude of the response does not appear to approach that of the input. Instead, a higher effective cubic damping results in a higher vibration level of the isolated mass at frequencies below the resonance frequency. It also does not reduce explicitly the response amplitude around the resonance frequency unlike the linear viscous damping. For a constant displacement amplitude random excitation, the excitation frequency bandwidth is found to be a significant factor in the level of effective cubic damping. A broader excitation bandwidth results in a higher level of cubic damping force.

The theoretical and numerical results for both harmonic and broadband excitation were validated experimentally. The experimental investigation was performed using a SDOF base excited vibration isolation system possessing a simple velocity feedback control active damper to reproduce the nonlinear damping force. The predictions were shown to be in good agreement with measurements thereby verifying the effects of cubic damping on a SDOF system undergoing harmonic and broadband base excitation.

PDF
Binder1.pdf - Other
Download (5MB)

More information

Published date: June 2014
Organisations: University of Southampton, Inst. Sound & Vibration Research

Identifiers

Local EPrints ID: 365357
URI: http://eprints.soton.ac.uk/id/eprint/365357
PURE UUID: 83e32ebb-5b7f-4f00-9293-4c1ea765337e
ORCID for Neil Ferguson: ORCID iD orcid.org/0000-0001-5955-7477

Catalogue record

Date deposited: 10 Jun 2014 09:12
Last modified: 06 Jun 2018 13:18

Export record

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×