Volume 38 Issue 3
Feb 2022
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JOURNAL OF MECHANICAL ENGINEERING  > 2022  >  38(3): 421525.
K. Liang, J. He, Z. Jia, and X. Zhang,Topology optimization of magnetorheological smart materials included PnCs for tunable wide bandgap design. Acta Mech. Sin., 2022, 38, http://www.w3.org/1999/xlink' xlink:href='https://doi.org/10.1007/s10409-021-09076-5'>https://doi.org/10.1007/s10409-021-09076-5
Citation: K. Liang, J. He, Z. Jia, and X. Zhang,Topology optimization of magnetorheological smart materials included PnCs for tunable wide bandgap design. Acta Mech. Sin., 2022, 38, http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1007/s10409-021-09076-5">https://doi.org/10.1007/s10409-021-09076-5
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Topology optimization of magnetorheological smart materials included PnCs for tunable wide bandgap design

doi: 10.1007/s10409-021-09076-5

  • State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China

Funds:

the National Natural Science Foundation of China Grant

More Information
  • Corresponding author: Zhang Xiaopeng, Email address: zhangxiaopeng@dlut.edu.cn (Xiaopeng Zhang)
  • Accepted Date: 11 Dec 2021
    • Available Online: 01 Aug 2022
  • Publish Date: 21 Feb 2022
  • Issue Publish Date: 01 Mar 2022
    Abstract
  • Design and application of tunable phononic crystals (PnCs) are attracting increasing interest due to their promising capabilities to manipulate acoustic and elastic waves effectively. This paper investigates topology optimization of the magnetorheological (MR) materials including PnCs for opening the tunable and wide bandgaps. Therein, the bandgap tunability of the PnCs is achieved by shear modulus variation of MR materials under a continuously changing applied magnetic field. The pseudo elemental densities representing the bi-material distribution inside the PnC unit cell are taken as design variables and interpolated with an artificial MR penalization model. An aggregated bandgap index for enveloping the extreme values of bandgap width and tunable range of the MR included smart PnCs is proposed as the objective function. In this context, the sensitivity analysis scheme is derived, and the optimization problem is solved with the gradient-based mathematical programming method. The effectiveness of the proposed optimization method is demonstrated by numerical examples, where the optimized solutions present tunable and stably wide bandgap characteristics under different magnetic fields. The tunable optimized PnCs based device that can provide a wider tunable bandgap range is also explored.

     

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    • References(52)
  • [1]
    S. Babaee, N. Viard, P. Wang, N. X. Fang, and K. Bertoldi, Harnessing deformation to switch on and off the propagation of sound, Adv. Mater. 28, 1631 26663556(2016).
    [2]
    K. Bertoldi, and M. C. Boyce, Mechanically triggered transformations of phononic band gaps in periodic elastomeric structures, Phys. Rev. B 77, 052105 (2008).
    [3]
    Z. Ren, L. Ji, R. Tao, M. Chen, Z. Wan, Z. Zhao, and D. Fang, SMP-based multi-stable mechanical metamaterials: From bandgap tuning to wave logic gates, Extreme Mech. Lett. 42, 101077 (2021).
    [4]
    R. Feng, and K. Liu, Tuning the band-gap of phononic crystals with an initial stress, Phys. B-Condensed Matter 407, 2032 (2012).
    [5]
    S. Ning, D. Chu, F. Yang, H. Jiang, Z. Liu, and Z. Zhuang, Characteristics of band gap and low-frequency wave propagation of mechanically tunable phononic crystals with scatterers in periodic porous elastomeric matrices, J. Appl. Mech. 88, 051001 (2021).
    [6]
    S. Zhang, Y. Shi, and Y. Gao, Tunability of band structures in a two-dimensional magnetostrictive phononic crystal plate with stress and magnetic loadings, Phys. Lett. A 381, 1055 (2017).
    [7]
    F. Allein, V. Tournat, V. E. Gusev, and G. Theocharis, Tunable magneto-granular phononic crystals, Appl. Phys. Lett. 108, 161903 (2016).
    [8]
    M. Ouisse, M. Collet, and F. Scarpa, A piezo-shunted kirigami auxetic lattice for adaptive elastic wave filtering, Smart Mater. Struct. 25, 115016 (2016).
    [9]
    Y. Song, and Y. Shen, A tunable phononic crystal system for elastic ultrasonic wave control, Appl. Phys. Lett. 118, 224104 (2021).
    [10]
    C. Nimmagadda, and K. H. Matlack, Thermally tunable band gaps in architected metamaterial structures, J. Sound Vib. 439, 29 (2019).
    [11]
    Z. Bian, W. Peng, and J. Song, Thermal tuning of band structures in a one-dimensional phononic crystal, J. Appl. Mech. 81, 041008 (2014).
    [12]
    O. Bou Matar, J. F. Robillard, J. O. Vasseur, A. C. Hladky-Hennion, P. A. Deymier, P. Pernod, and V. Preobrazhensky, Band gap tunability of magneto-elastic phononic crystal, J. Appl. Phys. 111, 054901 (2012).
    [13]
    Y. L. Wei, Q. S. Yang, and R. Tao, SMP-based chiral auxetic mechanical metamaterial with tunable bandgap function, Int. J. Mech. Sci. 195, 106267 (2021).
    [14]
    J. Zhu, H. Chen, B. Wu, W. Chen, and O. Balogun, Tunable band gaps and transmission behavior of SH waves with oblique incident angle in periodic dielectric elastomer laminates, Int. J. Mech. Sci. 146-147, 81 (2018).
    [15]
    W. P. Yang, and L. W. Chen, The tunable acoustic band gaps of two-dimensional phononic crystals with a dielectric elastomer cylindrical actuator, Smart Mater. Struct. 17, 015011 (2008).
    [16]
    G. Shmuel, Electrostatically tunable band gaps in finitely extensible dielectric elastomer fiber composites, Int. J. Solids Struct. 50, 680 (2013).
    [17]
    X. Zhou, and C. Chen, Tuning the locally resonant phononic band structures of two-dimensional periodic electroactive composites, Phys. B-Condensed Matter 431, 23 (2013).
    [18]
    J. Y. Yeh, Control analysis of the tunable phononic crystal with electrorheological material, Phys. B-Condensed Matter 400, 137 (2007).
    [19]
    L. W. Cai, D. K. Dacol, G. J. Orris, D. C. Calvo, and M. Nicholas, Acoustical scattering by multilayer spherical elastic scatterer containing electrorheological layer, J. Acoust. Soc. Am. 129, 12 21302983(2011).
    [20]
    A. Bayat, and F. Gordaninejad, Band-gap of a soft magnetorheological phononic crystal, J. Vib. Acoust. 137, 011011 (2015).
    [21]
    G. Zhang, and Y. Gao, Tunability of band gaps in two-dimensional phononic crystals with magnetorheological and electrorheological composites, Acta Mech. Solid Sin. 34, 40 (2021).
    [22]
    Y. Huang, C. L. Zhang, and W. Q. Chen, Tuning band structures of two-dimensional phononic crystals with biasing fields, J. Appl. Mech. 81, 091008 (2014).
    [23]
    N. Karami Mohammadi, P. I. Galich, A. O. Krushynska, and S. Rudykh, Soft magnetoactive laminates: large deformations, transverse elastic waves and band gaps tunability by a magnetic field, J. Appl. Mech. 86, 111001 (2019).
    [24]
    O. Sigmund, and K. Maute, Topology optimization approaches, Struct. Multidiscip. Optim. 48, 1031 (2013).
    [25]
    X. Huang, and Y. M. Xie, A further review of ESO type methods for topology optimization, Struct. Multidiscip. Optim. 41, 671 (2010).
    [26]
    G. Yi, and B. D. Youn, A comprehensive survey on topology optimization of phononic crystals, Struct. Multidiscip. Optim. 54, 1315 (2016).
    [27]
    W. Li, F. Meng, Y. Chen, Y. Li, and X. Huang, Topology optimization of photonic and phononic crystals and metamaterials: A review, Adv. Theor. Simul. 2, 1900017 (2019).
    [28]
    O. Sigmund, and J. S. Jensen, Systematic design of phononic band-gap materials and structures by topology optimization, Philos. Trans. R. Soc. London. Ser. A-Math. Phys. Eng. Sci. 361, 1001 12804226(2003).
    [29]
    X. Zhang, J. Xing, P. Liu, Y. Luo, and Z. Kang, Realization of full and directional band gap design by non-gradient topology optimization in acoustic metamaterials, Extreme Mech. Lett. 42, 101126 (2021).
    [30]
    Y. Chen, F. Meng, G. Sun, G. Li, and X. Huang, Topological design of phononic crystals for unidirectional acoustic transmission, J. Sound Vib. 410, 103 (2017).
    [31]
    J. He, and Z. Kang, Achieving directional propagation of elastic waves via topology optimization, Ultrasonics 82, 1 28732310(2018).
    [32]
    J. H. Park, P. S. Ma, and Y. Y. Kim, Design of phononic crystals for self-collimation of elastic waves using topology optimization method, Struct. Multidiscip. Optim. 51, 1199 (2015).
    [33]
    C. J. Rupp, A. Evgrafov, K. Maute, and M. L. Dunn, Design of phononic materials/structures for surface wave devices using topology optimization, Struct. Multidiscip. Optim. 34, 111 (2007).
    [34]
    H. W. Dong, S. D. Zhao, P. Wei, L. Cheng, Y. S. Wang, and C. Zhang, Systematic design and realization of double-negative acoustic metamaterials by topology optimization, Acta Mater. 172, 102 (2019).
    [35]
    R. E. Christiansen, F. Wang, and O. Sigmund, Topological insulators by topology optimization, Phys. Rev. Lett. 122, 234502 31298901(2019).
    [36]
    Y. Chen, F. Meng, and X. Huang, Creating acoustic topological insulators through topology optimization, Mech. Syst. Signal Process. 146, 107054 (2021).
    [37]
    Y. Luo, and J. Bao, A material-field series-expansion method for topology optimization of continuum structures, Comput. Struct. 225, 106122 (2019).
    [38]
    Y. Chen, X. Huang, G. Sun, X. Yan, and G. Li, Maximizing spatial decay of evanescent waves in phononic crystals by topology optimization, Comput. Struct. 182, 430 (2017).
    [39]
    A. Evgrafov, C. J. Rupp, M. L. Dunn, and K. Maute, Optimal synthesis of tunable elastic wave-guides, Comput. Methods Appl. Mech. Eng. 198, 292 (2008).
    [40]
    A. Shakeri, S. Darbari, and M. K. Moravvej-Farshi, Designing a tunable acoustic resonator based on defect modes, stimulated by selectively biased PZT rods in a 2D phononic crystal, Ultrasonics 92, 8 30216782(2019).
    [41]
    X. Zhang, H. Ye, N. Wei, R. Tao, and Z. Luo, Design optimization of multifunctional metamaterials with tunable thermal expansion and phononic bandgap, Mater. Des. 209, 109990 (2021).
    [42]
    S. L. Vatanabe, G. H. Paulino, and E. C. N. Silva, Maximizing phononic band gaps in piezocomposite materials by means of topology optimization, J. Acoust. Soc. Am. 136, 494 25096084(2014).
    [43]
    S. Hedayatrasa, K. Abhary, M. S. Uddin, and J. K. Guest, Optimal design of tunable phononic bandgap plates under equibiaxial stretch, Smart Mater. Struct. 25, 055025 (2016).
    [44]
    E. Bortot, O. Amir, and G. Shmuel, Topology optimization of dielectric elastomers for wide tunable band gaps, Int. J. Solids Struct. 143, 262 (2018).
    [45]
    G. Kreisselmeier, and R. Steinhauser, Systematic control design by optimizing a vector performance index, IFAC Proc. Volumes 12, 113 (1979).
    [46]
    X. Zhang, and Z. Kang, Topology optimization of magnetorheological fluid layers in sandwich plates for semi-active vibration control, Smart Mater. Struct. 24, 085024 (2015).
    [47]
    V. Rajamohan, R. Sedaghati, and S. Rakheja, Optimum design of a multilayer beam partially treated with magnetorheological fluid, Smart Mater. Struct. 19, 065002 (2010).
    [48]
    M. Stolpe, and K. Svanberg, An alternative interpolation scheme for minimum compliance topology optimization, Struct. Multidiscip. Optim. 22, 116 (2001).
    [49]
    S. Xu, Y. Cai, and G. Cheng, Volume preserving nonlinear density filter based on heaviside functions, Struct. Multidiscip. Optim. 41, 495 (2010).
    [50]
    X. Zhang, J. He, A. Takezawa, and Z. Kang, Robust topology optimization of phononic crystals with random field uncertainty, Int. J. Numer. Methods Eng. 115, 1154 (2018).
    [51]
    K. Wang, Y. Liu, and B. Wang, Ultrawide band gap design of phononic crystals based on topological optimization, Phys. B-Condens. Matter 571, 263 (2019).
    [52]
    B. Wu, R. Wei, and C. He, in Research on two-dimensional phononic crystal with magnetorheological material: Proceedings of IEEE international ultrasonics symposium, Beijing, 2008, pp. 1484-1486
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