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Fractional Maxwell Model of Viscoelastic Oscillator and Its Frequency Response

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Abstract

Background

Viscoelastic oscillator (VEO) is the basic element for viscoelastic damping structures and displays intermediate mechanical properties between purely Newton damping and purely Hooke spring. The modeling and prediction of the dynamic response of VEO are a challenging research task. Recently, fractional calculus is well used to model VEO and, however, fails to taking account into geometric factor by modeling the VEO as a rheological model.

Objective

Our objective was to establish a fractional Maxwell model of VEO (MFVEO) considering the geometric elements and derive its frequency response.

Method

The system equation of MFVEO was established by substituting the vibration equation and the geometric relation into the fractional Maxwell constitutive equation. The amplitude frequency function (AFF) and phase frequency function (PFF) of MFVEO were deduced by Laplace transform of fractional derivative as well as the linear and superposition properties. Finally, the variations of frequency responses of MFVEO under different system parameters were numerically studied.

Results

The system parameters, namely natural frequency, fractional orders, geometric factor and damping ratio, exert considerable effects on PFF and AFF of MFVEO at the specific frequency ratio. In addition, the harmonic peak exists for AFF and the corner frequency exists for PFF.

Conclusions

These results indicate that the frequency response of MFVEO is under influence of multiple factors and fractional orders; geometric factor should be optimized and designed for engineering applications.

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Acknowledgements

The work described in this paper was fully supported by the National Natural Science Foundation for Young Scientists of China (Grant Nos. 51305288 and 51405323) and the Taiyuan University of Science and Technology Foundation for Doctor (Grant Nos. 20162035 and 20122050).

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Authors and Affiliations

  1. College of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan, 030024, People’s Republic of China

    Zhan-Long Li, Zhi-qi Liu, Da-Gang Sun, Bi-Juan Yan & Jie Meng

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  1. Zhan-Long Li
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  2. Zhi-qi Liu
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  3. Da-Gang Sun
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  4. Bi-Juan Yan
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  5. Jie Meng
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Correspondence to Zhi-qi Liu.

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Li, ZL., Liu, Zq., Sun, DG. et al. Fractional Maxwell Model of Viscoelastic Oscillator and Its Frequency Response. J. Vib. Eng. Technol. 6, 1–6 (2018). https://doi.org/10.1007/s42417-018-0005-8

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  • DOI: https://doi.org/10.1007/s42417-018-0005-8

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