On dynamic properties of rubber isolators

• Main Author: Sjöberg, Mattias
• Format: Doctoral Thesis
• Language: English
• Published: KTH, Farkostteknik 2002
• Subjects: Rubber isolator; Dynamic stiffness; Nonlinear; Payne effect; Audible frequency; Fractional derivative; Mittag-Leffler function; Thermo-rheologically simple; Neo-Hooke
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3466

This work aims at enhancing the understanding and to provideimproved models of the dynamic behavior of rubber vibrationisolators which are widely used in mechanical systems.Initially, a time domainmodel relating compressions tocomponent forces accounting for preload effects, frequency anddynamic amplitude dependence is presented. The problem ofsimultaneously modelling the elastic, viscoelastic and frictionforces are removed by additively splitting them, where theelastic force response is modelled either by a fully linear ora nonlinear shape factor based approach, displaying resultsthat agree with those of a neo-Hookean hyperelastic isolatorunder a long term precompression. The viscoelastic force ismodelled by a fractional derivative element, while the frictionforce governs from a generalized friction element displaying asmoothed Coulomb force. This is a versatile one-dimensionalcomponent model effectively using a small number of parameterswhile exhibiting a good resemblance to measured isolatorcharacteristics. Additionally, the nonlinear excitationeffects on dynamic stiffness and damping of a filled rubberisolator are investigated through measurements. It is shownthat the well-known Payne effect - where stiffness is high forsmall excitation amplitudes and low for large amplitudes whiledamping displays a maximum at intermediate amplitudes -evaluated at a certain frequency, is to a large extentinfluenced by the existence of additional frequency componentsin the signal. Finally, a frequency, temperature and preloaddependent dynamic stiffness model is presented covering theranges from 20 to 20 000 Hz, -50 to +50 °C at 0 to 20 %precompression. A nearly incompressible, thermo-rheologicallysimple material model is adopted displaying viscoelasticitythrough a time - strain separable relaxation tensor with asingle Mittag-Leffler function embodying its time dependence.This fractional derivative based function successfully fitsmaterial properties throughout the whole audible frequencyrange. An extended neo-Hookean strain energy function, beingdirectly proportional to the temperature and density, isapplied for the finite deformation response with componentproperties solved by a nonlinear finite element procedure. Thepresented work is thus believed to enlighten workingconditions’impact on the dynamic properties of rubbervibration isolators, while additionally taking some of thesemost important features into account in the presentedmodels.