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Enhanced isolation performance of a high-static–low-dynamic stiffness isolator with geometric nonlinear damping

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Abstract

To enhance the low-frequency vibration isolation performance of the high-static–low-dynamic stiffness (HSLDS) isolator, a novel design of the geometric nonlinear damping (GND) comprising semi-active electromagnetic shunt damping is proposed. The GND is dependent on the vibration displacement and velocity, which can make the HSLDS isolator attain different damping characteristics in different frequency bands. Firstly, the configuration of the HSLDS isolator assembled with GND is presented, and then the restoring force, stiffness, and damping are derived. The dynamics of the mount under both base and force excitations are investigated based on the harmonic balance method, which are then verified by numerical simulations. After that, the effects of GND on the displacement and force transmissibility are studied, and the excellent performance caused by GND is analyzed based on the equivalent viscous damping mechanism. Finally, the comparison between the GND and cubic nonlinear damping is performed. The results demonstrate that the HSLDS isolator assembled with GND can realize the requirements of an isolation system under both base and force excitations of broadband vibration isolation performance and a low resonance peak with the high-frequency attenuation unaffected. Moreover, the GND outperforms the linear damping no matter the base excitation or force excitation is applied. For base excitation, the GND exhibits some desirable properties that the cubic nonlinear damping does not have at high frequencies.

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Abbreviations

GND:

Geometric nonlinear damping

EMSD:

Electromagnetic shunt damping

HSLDS:

High-static–low-dynamic stiffness

QZS:

Quasi-zero stiffness

NSM:

Negative stiffness mechanisms

DVDD:

Displacement–velocity-dependent damping

SFS:

Spiral flexure spring

MNSS:

Magnetic negative stiffness spring

MNS:

Magnetic negative stiffness

ED:

Electromagnetic devices

ENIC:

External negative impedance circuits

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Acknowledgements

This work is supported by the National Natural Science Foundation of China Academy of Engineering Physics and jointly set up “NSAF” joint fund (Grant No. U1630120).

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Authors and Affiliations

  1. State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiao Tong University, Xi’an, 710049, People’s Republic of China

    Guangxu Dong, Yahong Zhang, Yajun Luo, Shilin Xie & Xinong Zhang

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  1. Guangxu Dong
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  3. Yajun Luo
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  4. Shilin Xie
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  5. Xinong Zhang
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Correspondence to Xinong Zhang.

Appendix

Appendix

The integral expressions \(\varPhi _{1}\), \(\varPhi _{2}\), \(\varPhi _{3}\), and \(\varPhi _{4}\) in Eqs. (1–2) are given as follows:

$$\begin{aligned} \varPhi _1= & {} \frac{\cos \left( {\varphi _2 -\varphi _1 } \right) r\left( i \right) r_{\mathrm{in}2} }{\left| {r_{\mathrm{in}2}^2 +r^{2}\left( i \right) -2r_{\mathrm{in}2} r\left( i \right) \cos \left( {\varphi _2 -\varphi _1 } \right) +\left( {z_2 -z\left( k \right) } \right) ^{2}} \right| ^{1/2}} \end{aligned}$$
(49)
$$\begin{aligned} \varPhi _2= & {} \frac{\cos \left( {\varphi _2 -\varphi _1 } \right) r\left( i \right) r_{\mathrm{out}2} }{\left| {r_{\mathrm{out}2}^2 +r^{2}\left( i \right) -2r_{\mathrm{out}2} r\left( i \right) \cos \left( {\varphi _2 -\varphi _1 } \right) +\left( {z_2 -z\left( k \right) } \right) ^{2}} \right| ^{1/2}} \end{aligned}$$
(50)
$$\begin{aligned} \varPhi _3= & {} \frac{\left( {z_2 -z\left( k \right) } \right) \cos \left( {\varphi _2 -\varphi _1 } \right) r\left( i \right) r_{\mathrm{in}2} }{\left| {r_{\mathrm{in}2}^2 +r^{2}\left( i \right) -2r_{\mathrm{in}2} r\left( i \right) \cos \left( {\varphi _2 -\varphi _1 } \right) +\left( {z_2 -z\left( k \right) } \right) ^{2}} \right| ^{3/2}} \end{aligned}$$
(51)
$$\begin{aligned} \varPhi _4= & {} \frac{\left( {z_2 -z\left( k \right) } \right) \cos \left( {\varphi _2 -\varphi _1 } \right) r\left( i \right) r_{\mathrm{out}2} }{\left| {r_{\mathrm{out}2}^2 +r^{2}\left( i \right) -2r_{\mathrm{out}2} r\left( i \right) \cos \left( {\varphi _2 -\varphi _1 } \right) +\left( {z_2 -z\left( k \right) } \right) ^{2}} \right| ^{3/2}}\nonumber \\ \end{aligned}$$
(52)

where r(i) denotes the inner and outer radii of ring-shaped magnets with \(r(1)=r_{\mathrm{in}1}\) and \(r(2)=r_{\mathrm{out}1}\). The locations of top and bottom faces of moving magnet in inertial coordinate are represented with \(z(1)=z-h_{1}/2\) and \(z(2) =z-h_{1}/2\), separately.

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Dong, G., Zhang, Y., Luo, Y. et al. Enhanced isolation performance of a high-static–low-dynamic stiffness isolator with geometric nonlinear damping. Nonlinear Dyn 93, 2339–2356 (2018). https://doi.org/10.1007/s11071-018-4328-5

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  • DOI: https://doi.org/10.1007/s11071-018-4328-5

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