期刊
POLYMERS
卷 13, 期 11, 页码 -出版社
MDPI
DOI: 10.3390/polym13111703
关键词
natural rubber vibration isolator; waveguide model; mode matching; pre-compression; wide frequency range; transformation; fractional derivative; Mittag-Leffler function; resonance
资金
- European Commission under the programme FP5 Growth (NORMA) [GRD1-2000-25399]
A waveguide model is developed for a pre-compressed cylindrical natural rubber vibration isolator, with dynamic stiffness strongly depending on frequency and pre-compression, leading to resonance phenomena and low-frequency stiffness increases with higher pre-compressions. Good agreement with nonlinear finite element results is observed.
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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