Abstract
The gecko effect is famous for its smart adhesion, which is achieved by its fractal-like hierarchy from nano scale spatulas to micro scale seta. This paper designs a gecko-inspired receptor system for a three-dimensional printing technology. A fractal oscillator is established and solved for the fractal-like spring system, the experimental results show that any printed objects can be received smoothly without any morphology change.
Similar content being viewed by others
References
X.X. Li, Y.Y. Li, Y. Li, Gecko-like adhesion in the electrospinning process. Results Phys. 16, 102899 (2020)
X.X. Li, J.H. He, Nanoscale adhesion and attachment oscillation under the geometric potential. Part 1: the formation mechanism of nanofiber membrane in the electrospinning. Results Phys. 12, 1405–1410 (2019)
C.X. Wang, L. Xu, G.L. Liu, Y. Ren, J.C. Lv, D.W. Gao, Z.Q. Lu, Smart adhesion by surface treatment: experimental and theoretical insights. Therm. Sci. 23(4), 2355–2363 (2019)
V. Alizadehyazdi, M. Bonthron, M. Spenko, Optimizing electrostatic cleaning for dust removal on gecko-inspired adhesives. J. Electrostat. 108, 103499 (2020)
H.Y. Song, A thermodynamic model for a packing dynamical system. Therm. Sci. 24(4), 2331–2335 (2020)
Q.P. Ji, J. Wang, L.X. Lu, C.F. Ge, Li-He’s modified homotopy perturbation method coupled with the energy method for the dropping shock response of a tangent nonlinear packaging system. J. Low Freq. Noise V. A. 2020, 1461348420914457
W.X. Kuang, J. Wang, C.X. Huang, L.X. Lu, D. Gao, Z.W. Wang, C.F. Ge, Homotopy perturbation method with an auxiliary term for the optimal design of a tangent nonlinear packaging system. J. Low Freq. Noise V. A. 38(3–4), 1075–1080 (2019)
H.Y. Song, A modification of homotopy perturbation method for a hyperbolic tangent oscillator arising in nonlinear packaging system. J. Low Freq. Noise V. A. 38(3–4), 914–917 (2019)
Y.T. Zuo, H.J. Liu, A fractal rheological model for sic paste using a fractal derivative. J. Appl. Comput. Mech. 6(SI), 1434–1439 (2020)
Y.-T. Zuo, H.J-. Liu, Fractal approach to mechanical and electrical properties of graphene/sic composites. Facta Univ. Ser. Mech. Eng. (2021). https://doi.org/10.22190/FUME201212003Z
A. Gnatowski et al., The research of the thermal and mechanical properties of materials produced by 3D printing method. Therm. Sci. 23(4S), S1211–S1216 (2019)
L.Y. Xu, Y. Li, X.X. Li, J.H. He, Detection of cigarette smoke using a fiber membrane filmed with carbon nanoparticles and a fractal current law. Therm. Sci. 24(4), 2469–2474 (2020)
Z.P. Yang et al., A fractal model for pressure drop through a cigarette filter. Therm. Sci. 24(4), 2653–2659 (2020)
Y.K. Wu, Y. Liu, Fractal-like multiple jets in electrospinning process. Therm. Sci. 24(4), 2499–2505 (2020)
C.-H. He, J.H. He, H.M. Sedighi, Fangzhu (方诸): an ancient Chinese nanotechnology for water collection from air: History, mathematical insight, promises, and challenges. Math. Methods Appl. Sci. (2020). https://doi.org/10.1002/mma.6384
J.H. He, A new proof of the dual optimization problem and its application to the optimal material distribution of SiC/graphene composite. Rep. Mech. Eng. 1(1), 187–191 (2020). https://doi.org/10.31181/rme200101187h
C.-H. He, C. Liu, J.-H. He, A.H. Shirazi, H.M. Sedighi, Passive atmospheric water harvesting utilizing an ancient Chinese ink slab. Facta Universitatis-Ser. Mech. Eng. (2021). https://doi.org/10.22190/FUME201203001H
K.L. Wang, Effect of Fangzhu’s nano-scale surface morphology on water collection. Math. Methods Appl. Sci. (2020). https://doi.org/10.1002/mma.6569
J.-H. He, Y.O. El-Dib, Homotopy perturbation method for Fangzhu oscillator. J. Math. Chem. 58(10), 2245–2253 (2020)
J.H. He, Q.T. Ain, New promises and future challenges of fractal calculus: from two-scale thermodynamics to fractal variational principle. Therm. Sci. 24(2A), 659–681 (2020)
Q.T. Ain, J.H. He, On two-scale dimension and its applications. Therm. Sci. 23(3), 1707–1712 (2019)
J.H. He, Fractal calculus and its geometrical explanation. Results Phys. 10, 272–276 (2018)
Q.T. Ain, J.H. He, N. Anjum, M. Ali, The fractional complex transform: a novel approach to the time-fractional schrodinger equation. Fractals 28(7), 2050141 (2020)
J.H. He, Thermal science for the real world: reality and challenge. Therm. Sci. 24(4), 2289–2294 (2020)
K.L. Wang, C.F. Wei, A powerful and simple frequency formula to nonlinear fractal oscillators. J. Low Freq. Noise V. A. 1461348420947832 (2020)
D. Tian, Q.T. Ain, N. Anjum, Fractal N/MEMS: from pull-in instability to pull-in stability. Fractals (2020). https://doi.org/10.1142/S0218348X21500304
A. Elias-Zuniga, L.M. Palacios-Pineda, I.H. Jimenez-Cedeno, O. Martinez-Romero, D.O. Trejo, Equivalent power-form representation of the fractal Toda oscillator. Fractals (2020). https://doi.org/10.1142/S0218348X21500341
J.H. He, On the fractal variational principle for the Telegraph equation. Fractals (2021). https://doi.org/10.1142/S0218348X21500225
J.H. He, Y.O. El-Dib, The reducing rank method to solve third-order Duffing equation with the homotopy perturbation. Numer. Meth. Part. D. E. (2020). https://doi.org/10.1002/num.22609
D.N YU, J.H. He, A.G. Garcia, Homotopy perturbation method with an auxiliary parameter for nonlinear oscillators. J. Low Freq. Noise Vibration Active Control 38(3–4), 1540–1554 (2019)
J.H. He, Y.O. El-Dib, Periodic property of the time-fractional Kundu-Mukherjee-Naskar equation. Results Phys. 19, 103345 (2020)
N. Anjum, J.-H. He, Two modifications of the homotopy perturbation method for nonlinear oscillators. J. Appl. Comput. Mech. 6, 1420–1425 (2020). https://doi.org/10.22055/JACM.2020.34850.2482
J.H. He, Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B 20(10), 1141–1199 (2006)
J.-H. He, W.-F. Hou, N. Qie, K.A. Gepreel, A.H. Shirazi, H.M. Sedighi, Hamiltonian-based frequency-amplitude formulation for nonlinear oscillators. Facta Universitatis Ser. Mech. Eng. (2021). https://doi.org/10.22190/fume201205002H
N. Qie, W.-F. Hou, J.-H. He, The fastest insight into the large amplitude vibration of a string. Rep. Mech. Eng. 2(1), 1–5 (2020). https://doi.org/10.31181/rme200102001q
J.H. He, The simpler, the better: analytical methods for nonlinear oscillators and fractional oscillators. J. Low Freq. Noise V. A. 38(3–4), 1252–1260 (2019)
J.H. He, The simplest approach to nonlinear oscillators. Results Phys. 15, 102546 (2019). https://doi.org/10.1016/j.rinp.2019.102546
Y. Wang, S.W. Yao, H.W. Yang, A fractal derivative model for snow’s thermal insulation property. Therm. Sci. 23(4), 2351–2354 (2019)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author declared no potential conflicts of interest with respect to the research, authorship, and publication of this article.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zuo, Y. A gecko-like fractal receptor of a three-dimensional printing technology: a fractal oscillator. J Math Chem 59, 735–744 (2021). https://doi.org/10.1007/s10910-021-01212-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-021-01212-y