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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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Autores principales: Coja, Michael, Kari, Leif
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8197027/
https://www.ncbi.nlm.nih.gov/pubmed/34070970
http://dx.doi.org/10.3390/polym13111703
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author Coja, Michael
Kari, Leif
author_facet Coja, Michael
Kari, Leif
author_sort Coja, Michael
collection PubMed
description 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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spelling pubmed-81970272021-06-13 Using Waveguides to Model the Dynamic Stiffness of Pre-Compressed Natural Rubber Vibration Isolators Coja, Michael Kari, Leif Polymers (Basel) Article 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. MDPI 2021-05-23 /pmc/articles/PMC8197027/ /pubmed/34070970 http://dx.doi.org/10.3390/polym13111703 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Coja, Michael
Kari, Leif
Using Waveguides to Model the Dynamic Stiffness of Pre-Compressed Natural Rubber Vibration Isolators
title Using Waveguides to Model the Dynamic Stiffness of Pre-Compressed Natural Rubber Vibration Isolators
title_full Using Waveguides to Model the Dynamic Stiffness of Pre-Compressed Natural Rubber Vibration Isolators
title_fullStr Using Waveguides to Model the Dynamic Stiffness of Pre-Compressed Natural Rubber Vibration Isolators
title_full_unstemmed Using Waveguides to Model the Dynamic Stiffness of Pre-Compressed Natural Rubber Vibration Isolators
title_short Using Waveguides to Model the Dynamic Stiffness of Pre-Compressed Natural Rubber Vibration Isolators
title_sort using waveguides to model the dynamic stiffness of pre-compressed natural rubber vibration isolators
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8197027/
https://www.ncbi.nlm.nih.gov/pubmed/34070970
http://dx.doi.org/10.3390/polym13111703
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