Isotropic Dynamic Model of Coupling Spring and Shell Stiffnesses and Its Topology Optimization with Shear Resistance

Huang, Liangzheng; Zhang, Jinhao; Shang, Chao; Yang, Dongshuo; Fang, Xin

doi:10.3390/math14111876

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Isotropic Dynamic Model of Coupling Spring and Shell Stiffnesses and Its Topology Optimization with Shear Resistance

by

Liangzheng Huang

^1,2,

Jinhao Zhang

^1,2,*,

Chao Shang

³,

Dongshuo Yang

^1,2 and

Xin Fang

^1,2

¹

College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China

²

National Key Laboratory of Equipment State Sensing and Smart Support, National University of Defense Technology, Changsha 410073, China

³

Wuhan Second Ship Design and Research Institute, Wuhan 430205, China

^*

Author to whom correspondence should be addressed.

Mathematics 2026, 14(11), 1876; https://doi.org/10.3390/math14111876

Submission received: 21 April 2026 / Revised: 24 May 2026 / Accepted: 25 May 2026 / Published: 28 May 2026

(This article belongs to the Special Issue Advanced Mathematical Models in Engineering Design Optimization)

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Abstract

Dynamic vibration absorbers (DVAs) serve as critical passive control devices. However, their conventional designs are characterized by high directional sensitivity and large additional mass, failing to meet the rigorous demands of modern equipment for multi-directional coupled vibration suppression and lightweighting. To address these challenges, this study establishes an isotropic dynamic model of coupling spring and shell stiffnesses. This model shows that the isotropy degrades with the lightweight design due to a failure mode of shear deformation. Then, by constraining the shear stiffness, a collaborative design framework integrating topology optimization and parameter optimization is constructed to lighten the DVA. Using a 50 Hz DVA as a case study, prototype designs, simulations, and experiments are conducted. The results indicate that the isotropic natural frequencies agree well with the design targets. The shell mass is reduced by 79.8% compared to the conventional rigid shell design. Moreover, in vibration reduction simulations under the same total mass, the optimized absorber further reduces the vibration response by 7.4 dB compared to the rigid shell design.

Keywords: dynamic vibration absorber; lightweight; optimization

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MDPI and ACS Style

Huang, L.; Zhang, J.; Shang, C.; Yang, D.; Fang, X. Isotropic Dynamic Model of Coupling Spring and Shell Stiffnesses and Its Topology Optimization with Shear Resistance. Mathematics 2026, 14, 1876. https://doi.org/10.3390/math14111876

AMA Style

Huang L, Zhang J, Shang C, Yang D, Fang X. Isotropic Dynamic Model of Coupling Spring and Shell Stiffnesses and Its Topology Optimization with Shear Resistance. Mathematics. 2026; 14(11):1876. https://doi.org/10.3390/math14111876

Chicago/Turabian Style

Huang, Liangzheng, Jinhao Zhang, Chao Shang, Dongshuo Yang, and Xin Fang. 2026. "Isotropic Dynamic Model of Coupling Spring and Shell Stiffnesses and Its Topology Optimization with Shear Resistance" Mathematics 14, no. 11: 1876. https://doi.org/10.3390/math14111876

APA Style

Huang, L., Zhang, J., Shang, C., Yang, D., & Fang, X. (2026). Isotropic Dynamic Model of Coupling Spring and Shell Stiffnesses and Its Topology Optimization with Shear Resistance. Mathematics, 14(11), 1876. https://doi.org/10.3390/math14111876

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Isotropic Dynamic Model of Coupling Spring and Shell Stiffnesses and Its Topology Optimization with Shear Resistance

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