Using Waveguides to Model the Dynamic Stiffness of Pre-Compressed Natural Rubber Vibration Isolators

A waveguide model for a pre-compressed cylindrical natural rubber vibration isolator is developed within a wide frequency range—20 to 2000 Hz—and for a wide pre-compression domain—from vanishing to the maximum in service, that is 20%. The problems of simultaneously modeling the pre-compression and f...

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Bibliographic Details
Published inPolymers Vol. 13; no. 11; p. 1703
Main Authors Coja, Michael, Kari, Leif
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 23.05.2021
MDPI
Subjects
Boundary conditions
Equilibrium
Experiments
fractional derivative
Frequency ranges
Mechanical properties
Mittag-Leffler function
mode matching
Natural rubber
natural rubber vibration isolator
pre-compression
resonance
Rubber
Stiffness
Stress relaxation
transformation
Vibration
Vibration isolators
Viscoelasticity
waveguide model
Waveguides
wide frequency range
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Summary:A waveguide model for a pre-compressed cylindrical natural rubber vibration isolator is developed within a wide frequency range—20 to 2000 Hz—and for a wide pre-compression domain—from vanishing to the maximum in service, that is 20%. The problems of simultaneously modeling the pre-compression and frequency dependence are solved by applying a transformation of the pre-compressed isolator into a globally equivalent linearized, homogeneous, and isotropic form, thereby reducing the original, mathematically arduous, and complex problem into a vastly simpler assignment while using a straightforward waveguide approach to satisfy the boundary conditions by mode-matching. A fractional standard linear solid is applied as the visco-elastic natural rubber model while using a Mittag–Leffler function as the stress relaxation function. The dynamic stiffness is found to depend strongly on the frequency and pre-compression. The former is resulting in resonance phenomena such as peaks and troughs, while the latter exhibits a low-frequency magnitude stiffness increase in addition to peak and trough shifts with increased pre-compressions. Good agreement with nonlinear finite element results is obtained for the considered frequency and pre-compression range in contrast to the results of standard waveguide approaches.
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ISSN:2073-4360
2073-4360
DOI:10.3390/polym13111703