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Analytical study of a pneumatic quasi-zero-stiffness isolator with mistuned mass

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Abstract

Quasi-zero-stiffness (QZS) vibration isolation can increase the isolation frequency and improve the isolation performance by using a negative stiffness mechanism. However, most of the QZS isolation are sensitive to the loads applied for achieving effective isolation. This paper focuses on the dynamic phenomenon of the pneumatic QZS isolator with mistuned mass. A pneumatic QZS vibration isolator is proposed. The dynamic equation of the QZS vibration isolator under mass mistuning is derived. Amplitude–frequency relationship and force transmissibility are analyzed and simulated. It is observed that the system exhibits the possible response period and chaos phenomenon in the case of a large mass mistuning. It is very interesting that mass detuning will lead to a more complex nonlinear response of the QZS isolator, and the dynamic response will also be more sensitive to changes in parameters, such as external excitation frequency and amplitude, and damping ratio. The presented works will be helpful to improve the structure of the pneumatic QZS vibration isolator and determine the applicable working frequency of the isolator.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant No. 12072153), the Priority Academic Program Development of Jiangsu Higher Education Institutions and the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and astronautics) (Grant No. MCMS-I-0121G01), which are greatly appreciated.

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Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Junhan An, Guoping Chen, Tao Wang & Huan He

  2. Institute of Vibration Engineering Research, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Junhan An, Guoping Chen, Tao Wang & Huan He

  3. China Nuclear Power Technology Research Institute, Shenzhen, 518000, China

    Xi Deng & Chen Xi

  4. MIIT Key Laboratory of Multi-Functional Lightweight Materials and Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Huan He

  5. Laboratory of Aerospace Entry, Descent and Landing Technology, Beijing, 100094, China

    Huan He

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  1. Junhan An
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  2. Guoping Chen
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  3. Xi Deng
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  4. Chen Xi
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Correspondence to Huan He.

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Appendix

Appendix

If the second-order unstable region of the system is to be discussed, the solution form of Eq. (19) can be assumed as follows:

$$ \eta = s_{3} \cos \frac{\Omega T}{2} + s_{4} \sin \frac{\Omega T}{2} $$

Substituting it in Eq. (19), using the harmonic balance method, we can get the algebraic equations for the three undetermined parameters S0, S1, and S2, by writing them in the form of a matrix; it can be written as

$$ \left[ {\begin{array}{*{20}c} {\sigma_{0} - \frac{{\Omega^{2} }}{4} + \frac{{\sigma_{1} }}{2}\cos \Phi } & {\zeta \Omega - \frac{{\sigma_{1} }}{2}\sin \Phi } \\ { - \zeta \Omega - \frac{{\sigma_{1} }}{2}\sin \Phi } & {\sigma_{0} - \frac{{\Omega^{2} }}{4} - \frac{{\sigma_{1} }}{2}\cos \Phi } \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {s_{3} } \\ {s_{4} } \\ \end{array} } \right] = 0 $$

Similarly, the boundary of the second-order unstable zone can be obtained as follows:

$$ (\sigma_{0} - \frac{{\Omega^{2} }}{4})^{2} + \zeta^{2} \Omega^{2} - \frac{{\sigma_{1}^{2} }}{4} = 0 $$

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An, J., Chen, G., Deng, X. et al. Analytical study of a pneumatic quasi-zero-stiffness isolator with mistuned mass. Nonlinear Dyn 108, 3297–3312 (2022). https://doi.org/10.1007/s11071-022-07412-8

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