Axial audio-frequency stiffness of a bush mounting: the waveguide solution
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
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.
waveguide, non-mixed boundary condition, Mittag-Leffler, fractional derivative, audible frequency, bush mounting
IdentifiersURN: urn:nbn:se:kth:diva-5291DOI: 10.1016/j.apm.2005.08.008ISI: 000242415200004ScopusID: 2-s2.0-33749665802OAI: oai:DiVA.org:kth-5291DiVA: diva2:8330
QC 201010012005-06-072005-06-072016-05-18Bibliographically approved