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Time fractional calculus for liquid-path dynamic modelling of an isolator with a rubber element and high-viscosity silicone oil at low frequency

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Abstract

High-viscosity silicone oil has been widely used in dampers and isolators, such as those applications in civil engineering and heavy load locomotives. Prior study has shown that silicone oil properties play important roles for the dynamic characteristics of the liquid-filled isolator, incorporating a cylindrical rubber isolator coupled with an annular-orificed viscous damper. It exhibits significant frequency- as well as amplitude-dependent behaviour. To enhance modelling capabilities and better understand the underlying physics of the silicone-oil path of the isolator, this article makes attempts to model the dynamic behaviour of the liquid path applying time fractional calculus. Initially a fluid mechanics based model is derived incorporating fluid compressibility and rheological behaviour of silicone oil, which is described by a Maxwell model with arbitrary fractional-order derivatives of both the stress and strain. It is solved numerically in time domain by incorporating the discrete terms into the fourth-order Runge–Kutta algorithm. Compared with the conventional Maxwell fluid model, simulation results show an advantage for describing the dynamic behaviour of the isolator. Accordingly, two ‘global’, fractional-derivative, force–displacement models are proposed, which are more practical for vehicle system models. The five-parameter Zener model successfully captures the frequency-dependent behaviour of the liquid path. The superposition of two forces, defined by a fractional derivative Maxwell model and a duffing-type elastic force, to model the liquid path, is proposed to capture both the frequency- and amplitude-dependent properties of the isolator. The results show a better match to a certain extent for the amplitude-dependent property.

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Acknowledgements

The authors would like to acknowledge the financial supports from Science and Technology Innovation Program of Higher Education Institutions in Shanxi Province (Grant No. 2019L0644), Youth Fund Project of Shanxi Provincial Natural Science Foundation in China (Grant No. 20210302124698) and National Natural Science Foundation of China (Grant No. 11902207). Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect those of the supporting organizations.

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Authors and Affiliations

  1. School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan, 030024, Shanxi, China

    Xiaojuan Sun & Yumin Yang

  2. School of Mechanical Engineering, Southeast University, Nanjing, 211189, Jiangsu, China

    Qidi Fu

  3. School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang, 050043, Hebei, China

    Xin Liao

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  1. Xiaojuan Sun
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Sun, X., Yang, Y., Fu, Q. et al. Time fractional calculus for liquid-path dynamic modelling of an isolator with a rubber element and high-viscosity silicone oil at low frequency. Meccanica 57, 2849–2861 (2022). https://doi.org/10.1007/s11012-022-01597-3

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