Purpose This paper aims to quantify the nonlinear characteristics of quasi-zero stiffness (QZS) cruciform maglev isolators (CMI), including maglev forces, stiffness and vibration transmission. Method A multi-degree-of-freedom analytical model of CMI was built based on equivalent charge theory. The changes of maglev force and stiffness with vibration displacements, magnet geometry parameters and air gap were analyzed by using the model. The vibration transmission characteristics of CMI were quantitatively evaluated by applying an experiment-based method based on Volterra series and conditioned spectral analyses (CSA). Results It was revealed that vibration displacements have distinct nonlinear effects on the maglev forces and stiffness of CMI in both vertical and horizontal directions, and the effects are intercoupled with each other. For instance, the magnitude of vertical maglev force changes up to 12.17% due to the horizontal displacement <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2025_2043_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$x$</EquationSource> <EquationSource Format="MATHML"><math> <mi>x</mi> </math></EquationSource> </InlineEquation> when <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2025_2043_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">$y=4$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>y</mi> <mo>=</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation> mm, but only 1.16% when <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2025_2043_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">$y=2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>y</mi> <mo>=</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> mm. The sizes of magnets and air gap also have nonlinear influences on vertical maglev forces. However, the QZS property of CMI is robust to the geometric variations at the equilibrium point. The different order nonlinear vibration frequency responses of CMI were successfully identified under the conditions of random excitations in both vertical and horizontal directions. Conclusion The maglev forces and stiffness of CMI are distinctly influenced by vibration displacements, magnet geometry parameters and air gap. Most of the influences are nonlinear and intercoupled, leading to the CMI having nonlinear vibration transmission characteristics, which can be identified by using the method of Volterra series combined with CSA.

Nonlinear Dynamic Characteristics of Quasi-Zero Stiffness Cruciform Maglev Isolators

期刊论文
发表日期：

2025年8月15日

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Wentao Liu,
Jiafeng Wu,
Jiajia Zheng,
Shouren Wang,
Haiyan Shao

摘要

Purpose

This paper aims to quantify the nonlinear characteristics of quasi-zero stiffness (QZS) cruciform maglev isolators (CMI), including maglev forces, stiffness and vibration transmission.

Method

A multi-degree-of-freedom analytical model of CMI was built based on equivalent charge theory. The changes of maglev force and stiffness with vibration displacements, magnet geometry parameters and air gap were analyzed by using the model. The vibration transmission characteristics of CMI were quantitatively evaluated by applying an experiment-based method based on Volterra series and conditioned spectral analyses (CSA).

Results

It was revealed that vibration displacements have distinct nonlinear effects on the maglev forces and stiffness of CMI in both vertical and horizontal directions, and the effects are intercoupled with each other. For instance, the magnitude of vertical maglev force changes up to 12.17% due to the horizontal displacement $x$ $x$ when $y=4$ $y = 4$ mm, but only 1.16% when $y=2$ $y = 2$ mm. The sizes of magnets and air gap also have nonlinear influences on vertical maglev forces. However, the QZS property of CMI is robust to the geometric variations at the equilibrium point. The different order nonlinear vibration frequency responses of CMI were successfully identified under the conditions of random excitations in both vertical and horizontal directions.

Conclusion

The maglev forces and stiffness of CMI are distinctly influenced by vibration displacements, magnet geometry parameters and air gap. Most of the influences are nonlinear and intercoupled, leading to the CMI having nonlinear vibration transmission characteristics, which can be identified by using the method of Volterra series combined with CSA.