Similar articles

Abstract: Self-vibrating systems comprised of active materials have great potential for application in the fields of energy harvesting, actuation, bionic instrumentation, and autonomous robotics. However, it is challenging to obtain analytical solutions describing these systems, which hinders analysis and design. In this work, we propose a self-vibrating liquid crystal elastomer (LCE) fiber-spring system exposed to spatially-constant gradient light, and determine analytical solutions for its amplitude and period. First, using a dynamic model of LCE, we obtain the equations governing the self-vibration. Then, we analyze two different motion states and elucidate the mechanism of self-vibration. Subsequently, we derive analytical solutions for the amplitude and frequency using the multi-scale method, and compare the solutions with numerical results. The analytical outcomes are shown to be consistent with the numerical calculations, while taking far less computational time. Our findings reveal the utility of the multi-scale method in describing self-vibration, which may contribute to more efficient and accurate analyses of self-vibrating systems.

恒定梯度光下液晶弹性体纤维-弹簧自振系统的多尺度分析

[1]AllgowerEL, GeorgK, 1990. Numerical Continuation Methods: an Introduction. Springer, Berlin, Germany.

[2]BaiCP, KangJT, WangYQ, 2024. Light-induced motion of three-dimensional pendulum with liquid crystal elastomeric fiber. International Journal of Mechanical Science, 266:108911.

[3]BaumannA, Sánchez-FerrerA, JacomineL, et al., 2018. Motorizing fibres with geometric zero-energy modes. Nature Materials, 17(6):523-527.

[4]BazirA, BaumannA, ZiebertF, et al., 2020. Dynamics of fiberboids. Soft Matter, 16(22):5210-5223.

[5]BoissonadeJ, de KepperP, 2011. Multiple types of spatio-temporal oscillations induced by differential diffusion in the Landolt reaction. Physical Chemistry Chemical Physics, 13(9):4132-4137.

[6]ChakrabartiA, ChoiGPT, MahadevanL, 2020. Self-excited motions of volatile drops on swellable sheets. Physical Review Letters, 124(25):258002.

[7]ChenBH, LiuCY, XuZT, et al., 2024. Modeling the thermo-responsive behaviors of polydomain and monodomain nematic liquid crystal elastomers. Mechanics of Materials, 188:104838.

[8]ChenG, XianWK, WangQM, et al., 2021. Molecular simulation-guided and physics-informed mechanistic modeling of multifunctional polymers. Acta Mechanica Sinica, 37(5):725-745.

[9]ChengQB, ChengWY, DaiYT, et al., 2023. Self-oscillating floating of a spherical liquid crystal elastomer balloon under steady illumination. International Journal of Mechanical Science, 241:107985.

[10]ChengYC, LuHC, LeeX, et al., 2020. Kirigami-based light-induced shape-morphing and locomotion. Advanced Materials, 32(7):1906233.

[11]CheungYK, ChenSH, LauSL, 1990. Application of the incremental harmonic balance method to cubic non-linearity systems. Journal of Sound and Vibration, 140(2):273-286.

[12]CuiY, YinYF, WangCJ, et al., 2019. Transient thermo-mechanical analysis for bimorph soft robot based on thermally responsive liquid crystal elastomers. Applied Mathematics and Mechanics, 40(7):943-952.

[13]DaiL, WangLQ, ChenBH, et al., 2023. Shape memory behaviors of 3D printed liquid crystal elastomers. Soft Science, 3(1):5.

[14]DingWJ, 2010. Self-Excited Vibration. Springer, Berlin, Germany.

[15]FanST, ShenYJ, 2022. Extension of multi-scale method and its application to nonlinear viscoelastic system. Chinese Journal of Theoretical and Applied Mechanics, 54(2):495-502 (in Chinese).

[16]FangP, DaiLM, HouYJ, et al., 2019. The study of identification method for dynamic behavior of high-dimensional nonlinear system. Shock and Vibration, 2019:3497410.

[17]FuL, ZhaoWQ, MaJY, et al., 2022. A humidity-powered soft robot with fast rolling locomotion. Research, 2022:9832901.

[18]GeDL, DaiYT, LiK, 2023. Self-sustained Euler buckling of an optically responsive rod with different boundary constraints. Polymers, 15(2):316.

[19]GeFJ, YangR, TongX, et al., 2018. A multifunctional dye-doped liquid crystal polymer actuator: light-guided transportation, turning in locomotion, and autonomous motion. Angewandte Chemie International Edition, 57(36):11758-11763.

[20]GuoYL, LiuN, CaoQ, et al., 2022. Photothermal diol for NIR-responsive liquid crystal elastomers. ACS Applied Polymer Materials, 4(8):6202-6210.

[21]HaberJM, Sánchez-FerrerA, MihutAM, et al., 2013. Liquid-crystalline elastomer-nanoparticle hybrids with reversible switch of magnetic memory. Advanced Materials, 25(12):1787-1791.

[22]HarrisKD, BastiaansenCWM, LubJ, et al., 2005. Self-assembled polymer films for controlled agent-driven motion. Nano Letters, 5(9):1857-1860.

[23]HeQG, WangZJ, WangY, et al., 2021. Electrospun liquid crystal elastomer microfiber actuator. Science Robotics, 6(57):eabi9704.

[24]HeQG, YinR, HuaYC, et al., 2023. A modular strategy for distributed, embodied control of electronics-free soft robots. Science Advances, 9(27):eade9247.

[25]HellerMD, 2005. Hurwitz-based stability criteria for bounded nonlinear time-varying systems. International Conference on Control and Automation, p.942-947.

[26]HoMT, DattaA, BhattacharyyaSP, 1998. An elementary derivation of the Routh-Hurwitz criterion. IEEE Transactions on Automatic Control, 43(3):405-409.

[27]HuY, JiQX, HuangMJ, et al., 2021. Light-driven self-oscillating actuators with phototactic locomotion based on black phosphorus heterostructure. Angewandte Chemie International Edition, 60(37):20511-20517.

[28]HuaMT, KimC, DuYJ, et al., 2021. Swaying gel: chemo-mechanical self-oscillation based on dynamic buckling. Matter, 4(3):1029-1041.

[29]KageyamaY, IkegamiT, SatonagaS, et al., 2020. Light-driven flipping of azobenzene assemblies-sparse crystal structures and responsive behaviour to polarised light. Chemistry-A European Journal, 26(47):10759-10768.

[30]KimY, van den BergJ, CrosbyAJ, 2021. Autonomous snapping and jumping polymer gels. Nature Materials, 20(12):1695-1701.

[31]KumarK, KnieC, BlégerD, et al., 2016. A chaotic self-oscillating sunlight-driven polymer actuator. Nature Communications, 7(1):11975.

[32]LiJH, ZhangJY, GeW, et al., 2004. Multi-scale methodology for complex systems. Chemical Engineering Science, 59(8-9):1687-1700.

[33]LiMH, KellerP, LiB, et al., 2003. Light-driven side-on nematic elastomer actuators. Advanced Materials, 15(7-8):569-572.

[34]LiZW, MyungNV, YinYD, 2021. Light-powered soft steam engines for self-adaptive oscillation and biomimetic swimming. Science Robotics, 6(61):eabi4523.

[35]LiaoB, ZangHB, ChenMY, et al., 2020. Soft rod-climbing robot inspired by winding locomotion of snake. Soft Robotics, 7(4):500-511.

[36]LiaoW, YangZQ, 2022. The integration of sensing and actuating based on a simple design fiber actuator towards intelligent soft robots. Advanced Materials Technologies, 7(6):2101260.

[37]LiuJX, ShiF, SongWQ, et al., 2024. Modeling of self-oscillating flexible circuits based on liquid crystal elastomers. International Journal of Mechanical Science, 270:109099.

[38]MannaRK, ShklyaevOE, BalazsAC, 2021. Chemical pumps and flexible sheets spontaneously form self-regulating oscillators in solution. Proceedings of the National Academy of Sciences of the United States of America, 118(12):e2022987118.

[39]MärzR, 1984. On difference and shooting methods for boundary value problems in differential-algebraic equations. ZAMM-Journal of Applied Mathematics and Mechanics, 64(11):463-473.

[40]McLachlanRI, SunY, TsePSP, 2011. Linear stability of partitioned Runge-Kutta methods. SIAM Journal on Numerical Analysis, 49(1):232-263.

[41]NägeleT, HocheR, ZinthW, et al., 1997. Femtosecond photoisomerization of cis-azobenzene. Chemical Physics Letters, 272(5-6):489-495.

[42]NayfehAH, 1965. A perturbation method for treating nonlinear oscillation problems. Journal of Mathematics and Physics, 44(1-4):368-374.

[43]NayfehAH, 1993. Introduction to Perturbation Techniques. John Wiley & Sons, Berlin, Germany.

[44]NayfehAH, MookDT, 1979. Nonlinear Oscillations. John Wiley & Sons Inc., Germany.

[45]NayfehAH, PaiPF, 2008. Linear and Nonlinear Structural Mechanics. John Wiley & Sons Inc., Germany.

[46]NocentiniS, ParmeggianiC, MartellaD, et al., 2018. Optically driven soft micro robotics. Advanced Optical Materials, 6(14):1800207.

[47]PantonRL, 2013. Asymptotic analysis methods. In: Panton RL (Ed.), Incompressible Flow. 4th Edition. John Wiley and Sons, Inc., Hoboken, USA, p.374-408.

[48]PatidarKC, 2005. On the use of nonstandard finite difference methods. Journal of Difference Equations and Applications, 11(8):735-758.

[49]PivnenkoM, FedoryakoA, KutulyaL, et al., 1999. Resonance phenomena in a ferroelectric liquid crystal near the phase transition SmA-SmC. Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals, 328(14):111-118.

[50]PrestonDJ, JiangHJ, SanchezV, et al., 2019. A soft ring oscillator. Science Robotics, 4(31):eaaw5496.

[51]SerakS, TabiryanN, VergaraR, et al., 2010. Liquid crystalline polymer cantilever oscillators fueled by light. Soft Matter, 6(4):779-783.

[52]ShastriA, McGregorLM, LiuY, et al., 2015. An aptamer-functionalized chemomechanically modulated biomolecule catch-and-release system. Nature Chemistry, 7(5):447-454.

[53]SturrockPA, 1957. Non-linear effects in electron plasmas. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 242(1230):277-299.

[54]SunJH, WangYP, LiaoW, et al., 2021. Ultrafast, high-contractile electrothermal-driven liquid crystal elastomer fibers towards artificial muscles. Small, 17(44):2103700.

[55]ThomsonWT, DahlehMD, 2005. Theory of Vibration with Applications. 5th Edition. Pearson, Hoboken, USA.

[56]VestroniF, LuongoA, PaoloneA, 2008. A perturbation method for evaluating nonlinear normal modes of a piecewise linear two-degrees-of-freedom system. Nonlinear Dynamics, 54(4):379-393.

[57]WangLQ, WeiZX, XuZT, et al., 2023. Shape morphing of 3D printed liquid crystal elastomer structures with precuts. ACS Applied Polymer Materials, 5(9):7477-7484.

[58]WangXQ, TanCF, ChanKH, et al., 2018. In-built thermo-mechanical cooperative feedback mechanism for self-propelled multimodal locomotion and electricity generation. Nature Communications, 9(1):3438.

[59]WangY, XiaoJL, 2021. Confined thin film wrinkling on shape memory polymer with hybrid surface morphologies. Acta Mechanica Sinica, 37(7):1063-1071.

[60]WangYC, DangAL, ZhangZF, et al., 2020. Repeatable and reprogrammable shape morphing from photoresponsive gold nanorod/liquid crystal elastomers. Advanced Materials, 32(46):2004270.

[61]WangYC, LiuJQ, YangS, 2022. Multi-functional liquid crystal elastomer composites. Applied Physics Reviews, 9(1):011301.

[62]WangYC, YinR, JinLS, et al., 2023. 3D-printed photoresponsive liquid crystal elastomer composites for free-form actuation. Advanced Functional Materials, 33(4):2210614.

[63]WhiteTJ, TabiryanNV, SerakSV, et al., 2008. A high frequency photodriven polymer oscillator. Soft Matter, 4(9):1796-1798.

[64]WuHY, DaiYT, LiK, 2023. Self-vibration of liquid crystal elastomer strings under steady illumination. Polymers, 15(16):3483.

[65]WuHY, LouJF, ZhangB, et al., 2024a. Stability analysis of a liquid crystal elastomer self-oscillator under a linear temperature field. Applied Mathematics and Mechanics, 45(2):337-354.

[66]WuHY, ZhangB, LiK, 2024b. Synchronous behaviors of three coupled liquid crystal elastomer-based spring oscillators under linear temperature fields. Physical Review E, 109(2):024701.

[67]XuPB, ChenYQ, WuHY, et al., 2024a. Chaotic motion behaviors of liquid crystal elastomer pendulum under periodic illumination. Results in Physics, 56:107332.

[68]XuPB, ChenYQ, SunX, et al., 2024b. Light-powered self-sustained chaotic motion of a liquid crystal elastomer-based pendulum. Chaos, Solitons & Fractals, 184:115027.

[69]XuPB, SunX, DaiYT, et al., 2024c. Light-powered sustained chaotic jumping of a liquid crystal elastomer balloon. International Journal of Mechanical Science, 266:108922.

[70]YanZP, DaiHH, WangQS, et al., 2023. Harmonic balance methods: a review and recent developments. Computer Modeling in Engineering & Sciences, 137(2):1419-1459.

[71]YangHX, ZhangC, ChenBH, et al., 2023. Bioinspired design of stimuli-responsive artificial muscles with multiple actuation modes. Smart Materials and Structures, 32(8):085023.

[72]YoshidaR, 2010. Self-oscillating gels driven by the Belousov-Zhabotinsky reaction as novel smart materials. Advanced Materials, 22(31):3463-3483.

[73]YuY, DuCS, LiK, et al., 2022. Controllable and versatile self-motivated motion of a fiber on a hot surface. Extreme Mechanics Letters, 57:101918.

[74]YuY, HuHY, WuHY, et al., 2024a. A light-powered self-rotating liquid crystal elastomer drill. Heliyon, 10(6):e27748.

[75]YuY, HuHY, DaiYT, et al., 2024b. Modeling the light-powered self-rotation of a liquid crystal elastomer fiber-based engine. Physical Review E, 109(3):034701.

[76]YuY, ZhouL, DuCS, et al., 2024c. Self-galloping of a liquid crystal elastomer catenary cable under a steady temperature field. Thin-Walled Structures, 202:112071.

[77]ZengH, LahikainenM, LiuL, et al., 2019. Light-fuelled freestyle self-oscillators. Nature Communications, 10(1):5057.

[78]ZhouL, ChenHM, LiK, 2024. Optically-responsive liquid crystal elastomer thin film motors in linear/nonlinear optical fields. Thin-Walled Structures, 202:112082.

[79]ZuoW, SunTL, DaiYT, et al., 2023. Light-powered self-propelled trolley with a liquid crystal elastomer pendulum motor. International Journal of Solids and Structures, 285:112500.