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Axial audio-frequency stiffness of a bush mounting: the waveguide solution
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics.ORCID iD: 0000-0001-5760-3919
2007 (English)In: Applied Mathematical Modelling, ISSN 0307-904X, E-ISSN 1872-8480, Vol. 31, no 1, 38-53 p.Article in journal (Refereed) Published
Abstract [en]

An axial, dynamic stiffness model of an arbitrary wide and long rubber bush mounting is developed within the audible-frequency range, where influences of audible frequencies, material properties, bush mounting length and radius, are investigated. The problems of simultaneously satisfying the locally non-mixed boundary conditions at the radial and end surfaces are solved by adopting a waveguide approach, using the dispersion relation for axially symmetric waves in thick-walled infinite plates, while satisfying the radial boundary conditions by mode matching. The rubber is assumed nearly incompressible, displaying dilatation elasticity and deviatoric viscoelasticity based on a fractional derivative, standard linear solid embodying a Mittag-Leffler relaxation kernel, the main advantage being the minimum parameter number required to successfully model wide-frequency band material properties. The stiffness is found to depend strongly on frequency, displaying acoustical resonance phenomena; such as stiffness peaks and troughs. The presented model agrees fully with a simplified, long-bush model while diverging from it for increased diameter-to-length ratios. To a great extent, the increased influences of higher order modes and dispersion explain the discrepancies reported for the approximate approach.

Place, publisher, year, edition, pages
2007. Vol. 31, no 1, 38-53 p.
Keyword [en]
waveguide, non-mixed boundary condition, Mittag-Leffler, fractional derivative, audible frequency, bush mounting
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-5291DOI: 10.1016/j.apm.2005.08.008ISI: 000242415200004Scopus ID: 2-s2.0-33749665802OAI: oai:DiVA.org:kth-5291DiVA: diva2:8330
Note

QC 20101001

Available from: 2005-06-07 Created: 2005-06-07 Last updated: 2017-12-04Bibliographically approved
In thesis
1. Effective vibro-acoustical modelling of rubber isolators
Open this publication in new window or tab >>Effective vibro-acoustical modelling of rubber isolators
2005 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

This thesis, gathering four papers, concerns the enhancement in understanding and modelling of the audible dynamic stiffness of vibration rubber isolators including experimental measurements.

Paper A studies the performances of three different types of vibration isolator using an indirect measurement technique to estimate the blocked dynamic transfer stiffness of each specimen. The measurements are performed over a wide audible frequency range of 200 to 1000 Hz in a specially designed test rig enabling the investigation of arbitrary preload influences.

Paper B addresses the modelling of the audible-frequency stiffness of the rubber conical mount experimentally appraised in Paper A accounting for preload effects. The model is based on a simpliflied waveguide approach approximating the nonlinearities attributed to the predeformations by adopting shape factor considerations. The carbon black filled rubber is assumed incompressible, displaying a viscoelastic behavior based on a fractional derivative Kelvin-Voigt model efficiently reducing the number of required material parameters.

In Paper C the focus is on the axial dynamic stiffness modelling of an arbitrary long rubber bushing within the audible frequency range. The problems of simultaneously satisfying the locally non-mixed boundary conditions at the radial and end surfaces are solved by adopting a waveguide approach, using the dispersion relation for axially symmetric waves in thick-walled infinite plates, while fulfilling the radial boundary conditions by mode-matching. The results obtained are successfully compared with simpliflied models but display discrepancies when increasing the diameter-to-length ratios since the influence of higher order modes and dispersion augments.

Paper D develops an effective waveguide model for a pre-compressed cylindrical vibration isolator within the audible frequency domain at arbitrary compressions. The original, mathematically arduous problem of simultaneously modelling the preload and frequency dependence is solved by applying a novel transformation of the pre-strained isolator into a globally equivalent homogeneous and isotropic configuration enabling the straightforward application of a waveguide model to satisfy the boundary conditions. The results obtained present good agreement with the non-linear finite element results for a wide frequency range of 20 to 2000 Hz at different preloads.

Place, publisher, year, edition, pages
Stockholm: KTH, 2005. 25 p.
Series
Trita-AVE, ISSN 1651-7660 ; 2005:25
Keyword
Applied mechanics, Rubber isolator, Bush mounting, Dynamic stiffness, Waveguide, Fractional derivatives, Mode-matching, Pre-compressed, Prestrain, Preload, Predeformation, Viscoelasticity, Dispersion, Teknisk mekanik
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-266 (URN)91-7178-104-8 (ISBN)
Public defence
2005-06-16, D3, Lindstedtsvägen 5, Stockholm, 10:00
Opponent
Supervisors
Note
QC 20101001Available from: 2005-06-07 Created: 2005-06-07 Last updated: 2010-10-01Bibliographically approved

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