He's frequency formulation for fractal nonlinear oscillator arising in a microgravity space
At a microgravity condition, a spaceflight might be subject to a microgravity‐induced vibration. There is no theory so far to study the effect of microgravity on the vibration property. Here we give a fractal vibration model by the two‐scale thermodynamics. The fractal oscillator in the microgravity...
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| Published in | Numerical methods for partial differential equations Vol. 37; no. 2; pp. 1374 - 1384 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Hoboken, USA
John Wiley & Sons, Inc
01.03.2021
Wiley Subscription Services, Inc |
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| Online Access | Get full text |
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| Abstract | At a microgravity condition, a spaceflight might be subject to a microgravity‐induced vibration. There is no theory so far to study the effect of microgravity on the vibration property. Here we give a fractal vibration model by the two‐scale thermodynamics. The fractal oscillator in the microgravity space is modeled by using the fractal derivative, and its frequency is obtained by He's frequency formula. The variational principle of the fractal model is established by the fractal semi‐inverse method. The example shows that the proposed method is simple, efficient, and accurate. The frequency‐amplitude relationship is elucidated and the effect of the microgravity condition on vibration property is discussed. |
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| AbstractList | At a microgravity condition, a spaceflight might be subject to a microgravity‐induced vibration. There is no theory so far to study the effect of microgravity on the vibration property. Here we give a fractal vibration model by the two‐scale thermodynamics. The fractal oscillator in the microgravity space is modeled by using the fractal derivative, and its frequency is obtained by He's frequency formula. The variational principle of the fractal model is established by the fractal semi‐inverse method. The example shows that the proposed method is simple, efficient, and accurate. The frequency‐amplitude relationship is elucidated and the effect of the microgravity condition on vibration property is discussed. |
| Author | Wang, KangLe |
| Author_xml | – sequence: 1 givenname: KangLe orcidid: 0000-0002-6637-5687 surname: Wang fullname: Wang, KangLe email: kangle140917@163.com organization: Henan Polytechnic University |
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| Cites_doi | 10.1016/j.nonrwa.2007.10.002 10.1016/j.asej.2020.01.016 10.1186/s13662-020-02684-z 10.2298/TSCI190408138A 10.2298/TSCI200127065H 10.1016/j.rinp.2020.103031 10.1016/j.aej.2020.01.055 10.1177/1461348418818973 10.1142/S0218348X20500589 10.1016/j.aej.2020.04.019 10.3934/math.2020197 10.1142/S0218348X20500243 10.1007/s00707-019-02569-7 10.1016/j.aej.2013.09.005 10.1142/S0218348X19501342 10.1142/S0218348X19501226 10.1142/S0218348X20500310 10.1115/1.4043617 10.2298/TSCI1904163W 10.1016/j.rinp.2018.06.011 10.1515/ijnsns-2018-0362 10.2298/TSCI1904131H 10.1002/mma.6347 10.1142/S0218348X1850086X 10.1016/j.aml.2018.05.008 10.1177/1461348419844145 10.1108/HFF-05-2020-0247 10.1007/s10773-014-2123-8 10.1016/S0045-7825(99)00018-3 10.3389/fphy.2020.00064 10.1016/j.rinp.2019.102546 10.1016/j.apm.2013.11.035 10.1177/1461348418811028 10.1002/mma.6726 10.1142/S0218348X19500476 10.1002/mma.6297 10.1186/s13662-019-2488-3 10.1002/mma.6208 10.2298/TSCI1804871W 10.1002/mma.6335 |
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| References | 2019; 4 2010; 15 2015; 3 2019; 10 2019; 15 2019; 14 2020; 17 2019; 38 2020; 59 2018; 84 2018; 22 2020; 8 2018; 6 2020; 6 2020; 5 2020; 2020 2019; 20 2020 2019; 23 2013; 52 2014; 38 2020; 28 2019; 27 2020; 24 1999; 178 2020; 43 2018; 10 2020; 6(SI) 2014; 53 2019; 231 e_1_2_6_32_1 e_1_2_6_10_1 e_1_2_6_31_1 e_1_2_6_30_1 He J. H. (e_1_2_6_41_1) 2020; 6 e_1_2_6_19_1 Yang X. J. (e_1_2_6_5_1) 2015; 3 Li Z. B. (e_1_2_6_39_1) 2010; 15 He J. H. (e_1_2_6_44_1) 2020; 6 e_1_2_6_13_1 e_1_2_6_36_1 e_1_2_6_14_1 e_1_2_6_35_1 e_1_2_6_11_1 e_1_2_6_34_1 e_1_2_6_12_1 e_1_2_6_33_1 e_1_2_6_17_1 e_1_2_6_18_1 e_1_2_6_15_1 e_1_2_6_38_1 e_1_2_6_16_1 e_1_2_6_37_1 e_1_2_6_42_1 e_1_2_6_43_1 e_1_2_6_21_1 e_1_2_6_20_1 e_1_2_6_40_1 e_1_2_6_9_1 e_1_2_6_8_1 e_1_2_6_4_1 e_1_2_6_7_1 e_1_2_6_6_1 e_1_2_6_25_1 e_1_2_6_24_1 e_1_2_6_3_1 e_1_2_6_23_1 e_1_2_6_2_1 e_1_2_6_22_1 e_1_2_6_29_1 e_1_2_6_28_1 e_1_2_6_45_1 e_1_2_6_27_1 e_1_2_6_26_1 |
| References_xml | – volume: 20 start-page: 803 year: 2019 end-page: 809 article-title: A new investigation on fractional‐ordered neutral differential systems with state‐dependent delay publication-title: Int. J. Nonlinear Sci. Numer. Simul. – volume: 59 start-page: 1435 year: 2020 end-page: 1449 article-title: A model for describing the velocity of a particle in Brownian motion by Robotnov function based fractional operator publication-title: Alex. Eng. J. – volume: 27 year: 2019 article-title: Physical insight of local fractional calculus and its application to fractional Kdv‐burgers‐Kuramoto equation publication-title: Fractals – volume: 2020 start-page: 28 year: 2020 article-title: A modified analytical approach with existence and uniqueness for fractional Cauchy reaction–diffusion equations publication-title: Adv. Differ. Equ. – volume: 178 start-page: 257 year: 1999 end-page: 262 article-title: Homotopy perturbation technique publication-title: Comput. Methods Appl. Mech. Eng. – volume: 53 start-page: 3698 issue: 11 year: 2014 end-page: 3718 article-title: A tutorial review on fractal spacetime and fractional calculus publication-title: Int. J. Theor. Phy. – volume: 10 start-page: 272 year: 2018 end-page: 276 article-title: Fractal calculus and its geometrical explanation publication-title: Results. Phys. – volume: 2020 start-page: 252 year: 2020 article-title: A fractional derivative with two singular kernels and application to a heat conduction problem publication-title: Adv. Differ. Equ. – volume: 38 start-page: 1252 year: 2019 end-page: 1260 article-title: The simpler, the better: analytical methods for nonlinear oscillators and fractional oscillators publication-title: J. Low Freq. Noise V. A. – year: 2020 article-title: A fractional model for propagation of classical optical solitons by using nonsingular derivative publication-title: Math. Method. Appl. Sci. – volume: 10 start-page: 416 year: 2019 end-page: 427 article-title: Solution for an anti‐symmetric nonlinear oscillator by a modified He's homotopy perturbation method publication-title: Nonlinear Anal‐Real – volume: 6 start-page: 735 year: 2020 end-page: 740 article-title: Variational principle for the generalized KdV‐burgers equation with fractal derivatives for shallow water waves publication-title: J. Appl. Comput. Mech. – volume: 8 start-page: 64 year: 2020 article-title: Generalization of Caputo‐Fabrizio fractional derivative and applications to electrical circuits publication-title: Front. Phys. – volume: 38 start-page: 1540 issue: 3–4 year: 2019 end-page: 1554 article-title: Homotopy perturbation method with an auxiliary parameter for nonlinear oscillators publication-title: J. Low Freq. Noise Vib. Act. Control – volume: 52 start-page: 813 year: 2013 end-page: 819 article-title: A new fractional modeling arising in engineering sciences and its analytical approximate solution publication-title: Alex. Eng. J. – volume: 15 start-page: 970 year: 2010 end-page: 973 article-title: Fractional complex transform for fractional differential equations publication-title: Math. Comput. Appl. – volume: 27 year: 2019 article-title: A remark on Wang's fractal variational principle publication-title: Fractals – volume: 3 start-page: 752 year: 2015 end-page: 761 article-title: Local fractional homotopy perturbation method for solving fractal partial differential equations arising in mathematical physics publication-title: Rom. Rep. Phys. – volume: 23 start-page: 2163 issue: 4 year: 2019 end-page: 2170 article-title: Numerical method for fractional Zakharov‐Kuznetsov equation with He's fractional derivative publication-title: Therm. Sci. – volume: 38 start-page: 1060 year: 2019 end-page: 1074 article-title: He‐Laplace method for nonlinear vibration systems and nonlinear wave equations publication-title: J. Low. Freq. Noise. V. A. – volume: 28 year: 2020 article-title: A fractal variational theory for one‐dimensional compressible flow in a microgravity space publication-title: Fractals – volume: 6(SI) start-page: 1184 year: 2020 end-page: 1186 article-title: A simple approach to Volterra‐Fredholm integral equations publication-title: J. Appl. Comput. Mech. – volume: 14 year: 2019 article-title: A robust computational algorithm of homotopy asymptotic method for solving systems of fractional differential equations publication-title: J. Comput. Nonlinear Dyn. – year: 2020 article-title: Taylor series solution for a third order boundary value problem arising in architectural engineering publication-title: Ain Shams Eng. J. – volume: 59 start-page: 2891 year: 2020 end-page: 2899 article-title: New results on nonlocal functional integro‐differential equations via Hilfer fractional derivative publication-title: Alex. Eng. J. – volume: 28 year: 2020 article-title: On a high‐pass filter described by local fractional derivative publication-title: Fractals – volume: 43 start-page: 6062 year: 2020 end-page: 6080 article-title: An analysis for heat equations arises in diffusion process using new Yang‐Abdel‐Aty‐Cattani fractional operator publication-title: Math. Method .Appl. Sci. – volume: 4 year: 2019 article-title: A variational formulation for anisotropic wave traveling in a porous medium publication-title: Fractals – volume: 22 start-page: 1871 issue: 4 year: 2018 end-page: 1875 article-title: A modification of the reduced differential transform method for fractional calculus publication-title: Therm. Sci. – volume: 4 start-page: 1707 year: 2019 end-page: 1712 article-title: On two‐scale dimension and its applications publication-title: Therm. Sci. – volume: 5 start-page: 3035 year: 2020 end-page: 3055 article-title: A comparison study of two modified analytical approach for the solution of nonlinear fractional shallow water equations in fluid flow publication-title: AIMS Math. – volume: 38 start-page: 3154 year: 2014 end-page: 3163 article-title: A new analytical modelling for fractional telegraph equation via Laplace transform publication-title: Appl. Math. Model. – volume: 28 year: 2020 article-title: A fractal variational principle for the telegraph equation with fractal derivative publication-title: Fractals – volume: 84 start-page: 143 year: 2018 end-page: 147 article-title: A remark on Samuelson's variational principle in economics publication-title: Appl. Math. Lett. – year: 2020 article-title: Variational principle for nonlinear oscillator arising in a fractal nano/microelectromechanical system publication-title: Math. Method Appl. Sci. – volume: 17 year: 2020 article-title: Variational principle and periodic solution of the Kundu–Mukherjee–Naskar equation publication-title: Results Phys. – volume: 43 start-page: 5564 year: 2020 end-page: 5578 article-title: A study of fractional Lotka‐Volterra population model using Haar wavelet and Adams‐Bashforth‐Moulton methods publication-title: Math. Method. Appl. Sci. – volume: 23 start-page: 2131 issue: 4 year: 2019 end-page: 2133 article-title: Two‐scale mathematics and fractional calculus for thermodynamics publication-title: Therm. Sci. – volume: 43 start-page: 4460 year: 2020 end-page: 4471 article-title: A new Rabotnov fractional‐exponential function‐based fractional derivative for diffusion equation under external force publication-title: Math. Method. Appl. Sci. – year: 2020 article-title: A new fractal model for the soliton motion in a microgravity space publication-title: Int. J. Numer. Method. H. – volume: 231 start-page: 899 year: 2019 end-page: 906 article-title: Generalized variational principles for buckling analysis of circular cylinders publication-title: Acta Mech. – volume: 24 start-page: 659 year: 2020 end-page: 681 article-title: New promises and future challenges of fractal calculus: from two‐scale thermodynamics to fractal variational principle publication-title: Therm. Sci. – volume: 15 year: 2019 article-title: The simplest approach to nonlinear oscillators publication-title: Results. Phys – volume: 6 year: 2018 article-title: Fractal calculus and its application to explanation of biomechanism of polar bear hairs publication-title: Fractals – ident: e_1_2_6_2_1 doi: 10.1016/j.nonrwa.2007.10.002 – ident: e_1_2_6_9_1 doi: 10.1016/j.asej.2020.01.016 – ident: e_1_2_6_23_1 doi: 10.1186/s13662-020-02684-z – volume: 6 start-page: 1184 year: 2020 ident: e_1_2_6_44_1 article-title: A simple approach to Volterra‐Fredholm integral equations publication-title: J. Appl. Comput. Mech. – volume: 3 start-page: 752 year: 2015 ident: e_1_2_6_5_1 article-title: Local fractional homotopy perturbation method for solving fractal partial differential equations arising in mathematical physics publication-title: Rom. Rep. Phys. – ident: e_1_2_6_34_1 doi: 10.2298/TSCI190408138A – ident: e_1_2_6_37_1 doi: 10.2298/TSCI200127065H – ident: e_1_2_6_45_1 doi: 10.1016/j.rinp.2020.103031 – ident: e_1_2_6_13_1 doi: 10.1016/j.aej.2020.01.055 – ident: e_1_2_6_18_1 doi: 10.1177/1461348418818973 – ident: e_1_2_6_28_1 doi: 10.1142/S0218348X20500589 – ident: e_1_2_6_20_1 doi: 10.1016/j.aej.2020.04.019 – ident: e_1_2_6_11_1 doi: 10.3934/math.2020197 – ident: e_1_2_6_24_1 doi: 10.1142/S0218348X20500243 – ident: e_1_2_6_40_1 doi: 10.1007/s00707-019-02569-7 – ident: e_1_2_6_15_1 doi: 10.1016/j.aej.2013.09.005 – ident: e_1_2_6_31_1 doi: 10.1142/S0218348X19501342 – ident: e_1_2_6_35_1 doi: 10.1142/S0218348X19501226 – ident: e_1_2_6_38_1 doi: 10.1142/S0218348X20500310 – ident: e_1_2_6_7_1 doi: 10.1115/1.4043617 – ident: e_1_2_6_17_1 doi: 10.2298/TSCI1904163W – ident: e_1_2_6_29_1 doi: 10.1016/j.rinp.2018.06.011 – ident: e_1_2_6_16_1 doi: 10.1515/ijnsns-2018-0362 – ident: e_1_2_6_36_1 doi: 10.2298/TSCI1904131H – ident: e_1_2_6_22_1 doi: 10.1002/mma.6347 – ident: e_1_2_6_27_1 doi: 10.1142/S0218348X1850086X – volume: 15 start-page: 970 year: 2010 ident: e_1_2_6_39_1 article-title: Fractional complex transform for fractional differential equations publication-title: Math. Comput. Appl. – volume: 6 start-page: 735 year: 2020 ident: e_1_2_6_41_1 article-title: Variational principle for the generalized KdV‐burgers equation with fractal derivatives for shallow water waves publication-title: J. Appl. Comput. Mech. – ident: e_1_2_6_43_1 doi: 10.1016/j.aml.2018.05.008 – ident: e_1_2_6_33_1 doi: 10.1177/1461348419844145 – ident: e_1_2_6_25_1 doi: 10.1108/HFF-05-2020-0247 – ident: e_1_2_6_26_1 doi: 10.1007/s10773-014-2123-8 – ident: e_1_2_6_3_1 doi: 10.1016/S0045-7825(99)00018-3 – ident: e_1_2_6_19_1 doi: 10.3389/fphy.2020.00064 – ident: e_1_2_6_32_1 doi: 10.1016/j.rinp.2019.102546 – ident: e_1_2_6_14_1 doi: 10.1016/j.apm.2013.11.035 – ident: e_1_2_6_4_1 doi: 10.1177/1461348418811028 – ident: e_1_2_6_42_1 doi: 10.1002/mma.6726 – ident: e_1_2_6_30_1 doi: 10.1142/S0218348X19500476 – ident: e_1_2_6_8_1 doi: 10.1002/mma.6297 – ident: e_1_2_6_12_1 doi: 10.1186/s13662-019-2488-3 – ident: e_1_2_6_10_1 doi: 10.1002/mma.6208 – ident: e_1_2_6_6_1 doi: 10.2298/TSCI1804871W – ident: e_1_2_6_21_1 doi: 10.1002/mma.6335 |
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| Snippet | At a microgravity condition, a spaceflight might be subject to a microgravity‐induced vibration. There is no theory so far to study the effect of microgravity... |
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| StartPage | 1374 |
| SubjectTerms | fractal derivative Fractal models Fractals fractional differential equation frequency formulation Gravitational effects Inverse method Microgravity microgravity space Space flight two‐scale transform method Vibration |
| Title | He's frequency formulation for fractal nonlinear oscillator arising in a microgravity space |
| URI | https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fnum.22584 https://www.proquest.com/docview/2481896900 |
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