A Generalized Shape Function for Vibration Suppression Analysis of Acoustic Black Hole Beams Based on Fractional Calculus Theory
In this paper, a generalized acoustic black hole (ABH) beam covered with a viscoelastic layer is proposed to improve the energy dissipation based on the double-parameter Mittag–Leffler (ML) function. Since fractional-order constitutive models can more accurately capture the properties of viscoelasti...
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MDPI AG
2025-03-01
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| author | Jun Xu Ning Chen |
| author_facet | Jun Xu Ning Chen |
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| description | In this paper, a generalized acoustic black hole (ABH) beam covered with a viscoelastic layer is proposed to improve the energy dissipation based on the double-parameter Mittag–Leffler (ML) function. Since fractional-order constitutive models can more accurately capture the properties of viscoelastic materials, a fractional dynamic model of an ABH structure covered with viscoelastic film is established based on the fractional Kelvin–Voigt constitutive equation and the mechanical analysis of composite structures. To analyze the energy dissipation of the viscoelastic ML-ABH structures under steady-state conditions, the wave method is introduced, and the theory of vibration wave transmission in such non-uniform structures is extended. The effects of the fractional order, the film thickness and length, and shape function parameters on the dynamic characteristics of the ABH structure are systematically investigated. The study reveals that these parameters have a significant impact on the vibration characteristics of the ABH structure. To obtain the best parameters of the shape function under various parameters, the Particle Swarm Optimization (PSO) algorithm is employed. The results demonstrate that by selecting appropriate ML parameters and viscoelastic materials, the dissipation characteristics of the structure can be significantly improved. This research provides a theoretical foundation for structural vibration reduction in ABH structures. |
| format | Article |
| id | doaj-art-b56aeafbf8734fac9c6a7b6cf0f2483d |
| institution | DOAJ |
| issn | 2076-3417 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
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| series | Applied Sciences |
| spelling | doaj-art-b56aeafbf8734fac9c6a7b6cf0f2483d2025-08-20T02:53:02ZengMDPI AGApplied Sciences2076-34172025-03-01155276810.3390/app15052768A Generalized Shape Function for Vibration Suppression Analysis of Acoustic Black Hole Beams Based on Fractional Calculus TheoryJun Xu0Ning Chen1College of Intelligent Manufacturing, Anhui Vocational and Technical College, Hefei 230013, ChinaCollege of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, ChinaIn this paper, a generalized acoustic black hole (ABH) beam covered with a viscoelastic layer is proposed to improve the energy dissipation based on the double-parameter Mittag–Leffler (ML) function. Since fractional-order constitutive models can more accurately capture the properties of viscoelastic materials, a fractional dynamic model of an ABH structure covered with viscoelastic film is established based on the fractional Kelvin–Voigt constitutive equation and the mechanical analysis of composite structures. To analyze the energy dissipation of the viscoelastic ML-ABH structures under steady-state conditions, the wave method is introduced, and the theory of vibration wave transmission in such non-uniform structures is extended. The effects of the fractional order, the film thickness and length, and shape function parameters on the dynamic characteristics of the ABH structure are systematically investigated. The study reveals that these parameters have a significant impact on the vibration characteristics of the ABH structure. To obtain the best parameters of the shape function under various parameters, the Particle Swarm Optimization (PSO) algorithm is employed. The results demonstrate that by selecting appropriate ML parameters and viscoelastic materials, the dissipation characteristics of the structure can be significantly improved. This research provides a theoretical foundation for structural vibration reduction in ABH structures.https://www.mdpi.com/2076-3417/15/5/2768ABH structureML functionwave methodvibration energy reductionaccumulationfractional calculus |
| spellingShingle | Jun Xu Ning Chen A Generalized Shape Function for Vibration Suppression Analysis of Acoustic Black Hole Beams Based on Fractional Calculus Theory Applied Sciences ABH structure ML function wave method vibration energy reduction accumulation fractional calculus |
| title | A Generalized Shape Function for Vibration Suppression Analysis of Acoustic Black Hole Beams Based on Fractional Calculus Theory |
| title_full | A Generalized Shape Function for Vibration Suppression Analysis of Acoustic Black Hole Beams Based on Fractional Calculus Theory |
| title_fullStr | A Generalized Shape Function for Vibration Suppression Analysis of Acoustic Black Hole Beams Based on Fractional Calculus Theory |
| title_full_unstemmed | A Generalized Shape Function for Vibration Suppression Analysis of Acoustic Black Hole Beams Based on Fractional Calculus Theory |
| title_short | A Generalized Shape Function for Vibration Suppression Analysis of Acoustic Black Hole Beams Based on Fractional Calculus Theory |
| title_sort | generalized shape function for vibration suppression analysis of acoustic black hole beams based on fractional calculus theory |
| topic | ABH structure ML function wave method vibration energy reduction accumulation fractional calculus |
| url | https://www.mdpi.com/2076-3417/15/5/2768 |
| work_keys_str_mv | AT junxu ageneralizedshapefunctionforvibrationsuppressionanalysisofacousticblackholebeamsbasedonfractionalcalculustheory AT ningchen ageneralizedshapefunctionforvibrationsuppressionanalysisofacousticblackholebeamsbasedonfractionalcalculustheory AT junxu generalizedshapefunctionforvibrationsuppressionanalysisofacousticblackholebeamsbasedonfractionalcalculustheory AT ningchen generalizedshapefunctionforvibrationsuppressionanalysisofacousticblackholebeamsbasedonfractionalcalculustheory |