Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam
In this paper, an effective numerical algorithm is proposed for the first time to solve the fractional visco-elastic rotating beam in the time domain. On the basis of fractional derivative Kelvin–Voigt and fractional derivative element constitutive models, the two governing equations of fractional v...
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| Vydáno v: | Chaos, solitons and fractals Ročník 132; s. 109585 |
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| Jazyk: | angličtina |
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Elsevier Ltd
01.03.2020
Elsevier |
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| ISSN: | 0960-0779, 1873-2887 |
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| Abstract | In this paper, an effective numerical algorithm is proposed for the first time to solve the fractional visco-elastic rotating beam in the time domain. On the basis of fractional derivative Kelvin–Voigt and fractional derivative element constitutive models, the two governing equations of fractional visco-elastic rotating beams are established. According to the approximation technique of shifted Chebyshev polynomials, the integer and fractional differential operator matrices of polynomials are derived. By means of the collocation method and matrix technique, the operator matrices of governing equations can be transformed into the algebraic equations. In addition, the convergence analysis is performed. In particular, unlike the existing results, we can get the displacement and the stress numerical solution of the governing equation directly in the time domain. Finally, the sensitivity of the algorithm is verified by numerical examples. |
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| AbstractList | In this paper, an effective numerical algorithm is proposed for the first time to solve the fractional visco-elastic rotating beam in the time domain. On the basis of fractional derivative Kelvin–Voigt and fractional derivative element constitutive models, the two governing equations of fractional visco-elastic rotating beams are established. According to the approximation technique of shifted Chebyshev polynomials, the integer and fractional differential operator matrices of polynomials are derived. By means of the collocation method and matrix technique, the operator matrices of governing equations can be transformed into the algebraic equations. In addition, the convergence analysis is performed. In particular, unlike the existing results, we can get the displacement and the stress numerical solution of the governing equation directly in the time domain. Finally, the sensitivity of the algorithm is verified by numerical examples. In this paper, an effective numerical algorithm is proposed for the first time to solve the fractional visco-elastic rotating beam in the time domain. On the basis of fractional derivative Kelvin-Voigt and fractional derivative element con-stitutive models, the two governing equations of fractional visco-elastic rotating beams are established. According to the approximation technique of shifted Chebyshev polynomials, the integer and fractional differential operator matrices of polynomials are derived. By means of the collocation method and matrix technique, the operator matrices of governing equations can be transformed into the algebraic equations. In addition, the convergence analysis is performed. In particular, unlike the existing results, we can get the displacement and the stress numerical solution of the governing equation directly in the time domain. Finally, the sensitivity of the algorithm is verified by numerical examples. |
| ArticleNumber | 109585 |
| Author | Wang, Lei Chen, Yi-Ming |
| Author_xml | – sequence: 1 givenname: Lei surname: Wang fullname: Wang, Lei email: qiqiqiqiha@163.com organization: School of Sciences, Yanshan University, Qinhuangdao, Hebei 066004, PR China – sequence: 2 givenname: Yi-Ming surname: Chen fullname: Chen, Yi-Ming email: chenym@ysu.edu.cn organization: School of Sciences, Yanshan University, Qinhuangdao, Hebei 066004, PR China |
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| Cites_doi | 10.1016/j.jsv.2010.09.017 10.1109/TAC.2015.2449151 10.1002/nme.2003 10.1122/1.549887 10.1080/00207160.2018.1438604 10.1016/j.compstruc.2013.02.011 10.1007/s10665-013-9642-9 10.1515/fca-2018-0079 10.1016/j.ijsolstr.2013.06.010 10.1016/j.apacoust.2019.05.008 10.1093/gji/ggu491 10.1016/j.ijnonlinmec.2015.05.004 10.1002/andp.200751907-803 10.1016/j.apm.2016.04.011 10.1364/AO.56.001591 10.1615/CritRevBiomedEng.v35.i6.10 10.1016/j.proeng.2017.09.041 10.1016/j.jsv.2006.06.040 10.1007/s00419-015-1019-2 10.1109/TFUZZ.2019.2895560 10.1016/j.camwa.2016.05.002 10.1016/j.physa.2006.04.034 10.1007/s11760-015-0856-3 10.1016/S0960-0779(98)00302-6 10.1002/nme.1840 10.1016/j.chaos.2006.07.051 10.1016/j.apm.2009.08.022 10.1016/j.jcp.2005.08.008 10.1038/srep03431 10.1016/j.ijmecsci.2014.03.007 10.1016/j.ijmecsci.2018.04.049 10.1007/s12206-016-0306-3 10.1016/j.jsv.2017.03.032 10.1016/j.compstruct.2015.06.038 10.1109/TFUZZ.2018.2883374 10.1016/j.jcp.2007.02.001 10.1016/j.jsv.2018.04.027 10.1016/j.jare.2015.06.004 |
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| Keywords | Fractional visco-elastic rotating beam Fractional governing equation Approximation technique Operator matrix Numerical solution Shifted Chebyshev polynomials |
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| References | Chen, Liu, Li, Sun (bib0037) 2014; 238 Magdalena, Lewandowski (bib0019) 2017; 199 Tian, Su, Kai, Hua (bib0044) 2018; 426 Chen (bib0005) 2008; 36 Zaicenco (bib0040) 2015; 200 Lewandowski, Baum (bib0014) 2015; 85 Lewandowski, Pawlak (bib0010) 2011; 330 Lewandowski, Wielentejczyk (bib0013) 2017; 339 Kang, Zhou, Liu, Liu (bib0011) 2015 Bazoune (bib0045) 2014; 14 Xie, Yao, Gui, Zhao, Li (bib0033) 2018; 332 Permoon, Rashidinia, Parsa, Haddadpour, Salehi (bib0024) 2016; 30 Bahraini, Farid, Ghavanloo (bib0016) 2013; 27 Fernanda, Miguel, Higinio (bib0038) 2018; 21 Demir, Bildik, Snr (bib0023) 2014; 85 Xu, Jiang (bib0047) 2017; 73 Bagley, Torvik (bib0008) 1986; 30 Lorenzo, Hartley (bib0003) 2007; 35 Chen, Sun, Li, Fu (bib0034) 2013; 90 Suman, Kumar, Singh (bib0039) 2016; 10 Protasov, Jungers (bib0042) 2016; 61 Chang, Lin, Huang, Choi (bib0021) 2010; 34 Chen, Du (bib0049) 2019; 155 Gemant (bib0007) 1938; 25 Tadjeran, Meerschaert, Scheffler (bib0030) 2006; 213 Qiu, Sun, Rudas, Gao (bib0029) 2019 Wang, Xu, Wei, Xie (bib0035) 2018; 96 Srivatsa, Ganguli (bib0043) 2018; 142-143 Gioacchino, Mario, Giuseppe (bib0012) 2018; 131 Lin, Xu (bib0048) 2007; 255 Martin (bib0025) 2016; 40 Paola, Heuer, Pirrotta (bib0017) 2013; 50 Ramirez (bib0002) 2010; 16 Akritas, Antoniou, Ivanov (bib0026) 2000; 11 Friswell, Adhikari, Lei (bib0022) 2007; 71 Chen, Sun, Liu (bib0032) 2014; 244 Sweilam, Almekhlafi (bib0001) 2016; 7 Sun, Mou, Qiu, Wang, Gao (bib0027) 2019; 27 Banerjee, Su, Jackson (bib0046) 2006; 298 Kiasat, Zamani, Aghdam (bib0020) 2014; 83 Meng, Yi, Huang, Lei (bib0031) 2018; 336 Leung, Yang, Zhu, Guo (bib0009) 2013; 121 Xing, Guo (bib0041) 2017; 56 He, Rafiee, Mareishi, Liew (bib0018) 2015; 131 Du, Wang, Hu (bib0006) 2013; 3 Meerschaert, Scalas (bib0004) 2006; 370 Cortes, Elejabarrieta (bib0015) 2007; 69 Qiu, Sun, Wang, Gao (bib0028) 2019; 27 Chen, Liu, Liu, Boutat (bib0036) 2016 Ramirez (10.1016/j.chaos.2019.109585_bib0002) 2010; 16 Tian (10.1016/j.chaos.2019.109585_bib0044) 2018; 426 Chen (10.1016/j.chaos.2019.109585_bib0034) 2013; 90 He (10.1016/j.chaos.2019.109585_bib0018) 2015; 131 Protasov (10.1016/j.chaos.2019.109585_bib0042) 2016; 61 Chen (10.1016/j.chaos.2019.109585_bib0005) 2008; 36 Bagley (10.1016/j.chaos.2019.109585_bib0008) 1986; 30 Sweilam (10.1016/j.chaos.2019.109585_bib0001) 2016; 7 Lewandowski (10.1016/j.chaos.2019.109585_bib0014) 2015; 85 Cortes (10.1016/j.chaos.2019.109585_bib0015) 2007; 69 Banerjee (10.1016/j.chaos.2019.109585_bib0046) 2006; 298 Leung (10.1016/j.chaos.2019.109585_bib0009) 2013; 121 Bahraini (10.1016/j.chaos.2019.109585_bib0016) 2013; 27 Paola (10.1016/j.chaos.2019.109585_bib0017) 2013; 50 Lewandowski (10.1016/j.chaos.2019.109585_bib0010) 2011; 330 Chen (10.1016/j.chaos.2019.109585_bib0049) 2019; 155 Meerschaert (10.1016/j.chaos.2019.109585_bib0004) 2006; 370 Demir (10.1016/j.chaos.2019.109585_bib0023) 2014; 85 Gemant (10.1016/j.chaos.2019.109585_bib0007) 1938; 25 Permoon (10.1016/j.chaos.2019.109585_bib0024) 2016; 30 Qiu (10.1016/j.chaos.2019.109585_bib0029) 2019 Chen (10.1016/j.chaos.2019.109585_bib0032) 2014; 244 Fernanda (10.1016/j.chaos.2019.109585_bib0038) 2018; 21 Kiasat (10.1016/j.chaos.2019.109585_bib0020) 2014; 83 Chang (10.1016/j.chaos.2019.109585_bib0021) 2010; 34 Meng (10.1016/j.chaos.2019.109585_bib0031) 2018; 336 Xie (10.1016/j.chaos.2019.109585_bib0033) 2018; 332 Qiu (10.1016/j.chaos.2019.109585_bib0028) 2019; 27 Zaicenco (10.1016/j.chaos.2019.109585_bib0040) 2015; 200 Suman (10.1016/j.chaos.2019.109585_bib0039) 2016; 10 Lin (10.1016/j.chaos.2019.109585_bib0048) 2007; 255 Martin (10.1016/j.chaos.2019.109585_bib0025) 2016; 40 Tadjeran (10.1016/j.chaos.2019.109585_bib0030) 2006; 213 Lewandowski (10.1016/j.chaos.2019.109585_bib0013) 2017; 339 Srivatsa (10.1016/j.chaos.2019.109585_bib0043) 2018; 142-143 Gioacchino (10.1016/j.chaos.2019.109585_bib0012) 2018; 131 Chen (10.1016/j.chaos.2019.109585_bib0036) 2016 Du (10.1016/j.chaos.2019.109585_bib0006) 2013; 3 Friswell (10.1016/j.chaos.2019.109585_bib0022) 2007; 71 Magdalena (10.1016/j.chaos.2019.109585_bib0019) 2017; 199 Xu (10.1016/j.chaos.2019.109585_bib0047) 2017; 73 Lorenzo (10.1016/j.chaos.2019.109585_bib0003) 2007; 35 Chen (10.1016/j.chaos.2019.109585_bib0037) 2014; 238 Bazoune (10.1016/j.chaos.2019.109585_bib0045) 2014; 14 Kang (10.1016/j.chaos.2019.109585_bib0011) 2015 Sun (10.1016/j.chaos.2019.109585_bib0027) 2019; 27 Wang (10.1016/j.chaos.2019.109585_bib0035) 2018; 96 Xing (10.1016/j.chaos.2019.109585_bib0041) 2017; 56 Akritas (10.1016/j.chaos.2019.109585_bib0026) 2000; 11 |
| References_xml | – volume: 21 start-page: 1506 year: 2018 end-page: 1523 ident: bib0038 article-title: Extrapolating for attaining high precision solutions for fractional partial differential equations[j] publication-title: Fract Calculus Appl Anal – volume: 61 start-page: 795 year: 2016 end-page: 798 ident: bib0042 article-title: Analysing the stability of linear systems via exponential chebyshev polynomials publication-title: IEEE Trans Autom Control – volume: 85 start-page: 1793 year: 2015 end-page: 1814 ident: bib0014 article-title: Dynamic characteristics of multilayered beams with viscoelastic layers described by the fractional zener model publication-title: Arch Appl Mech – volume: 27 start-page: 2152 year: 2019 end-page: 2161 ident: bib0028 article-title: Observer-based fuzzy adaptive event-triggered control for pure-feedback nonlinear systems with prescribed performance publication-title: IEEE Trans Fuzzy Syst – volume: 155 start-page: 1 year: 2019 end-page: 15 ident: bib0049 article-title: A fourier series solution for the transverse vibration of rotating beams with elastic boundary supports publication-title: Appl Acoust – volume: 298 start-page: 1034 year: 2006 end-page: 1054 ident: bib0046 article-title: Free vibration of rotating tapered beams using the dynamic stiffness method publication-title: J Sound Vib – volume: 142-143 start-page: 440 year: 2018 end-page: 455 ident: bib0043 article-title: Non-rotating beams isospectral to rotating rayleigh beams publication-title: Int J Mech Sci – volume: 199 start-page: 366 year: 2017 end-page: 371 ident: bib0019 article-title: Sensitivity analysis of dynamic characteristics of composite beams with viscoelastic layers publication-title: Proc Eng – volume: 14 start-page: 169 year: 2014 end-page: 179 ident: bib0045 article-title: Effect of tapering on natural frequencies of rotating beams publication-title: Shock Vib – volume: 27 start-page: 1063 year: 2013 end-page: 1070 ident: bib0016 article-title: Large deflection of viscoelastic beams using fractional derivative model publication-title: J Eng Math – volume: 71 start-page: 1365 year: 2007 end-page: 1386 ident: bib0022 article-title: Vibration analysis of beams with non-local foundations using the finite element method publication-title: Int J Numer Methods Eng – volume: 40 start-page: 7988 year: 2016 end-page: 7995 ident: bib0025 article-title: A modified variational iteration method for the analysis of viscoelastic beams publication-title: Appl Math Model – volume: 213 start-page: 205 year: 2006 end-page: 213 ident: bib0030 article-title: A second-order accurate numerical approximation for the fractional diffusion equation publication-title: J Comput Phys – volume: 332 start-page: 197 year: 2018 end-page: 208 ident: bib0033 article-title: A two-dimensional Chebyshev wavelets approach for solving the Fokker–Planck equations of time and space fractional derivatives type with variable coefficients publication-title: Appl Math Comput – volume: 131 start-page: 102 year: 2018 end-page: 110 ident: bib0012 article-title: On the dynamics of non-local fractional viscoelastic beams under stochastic agencies publication-title: Compos B: Eng – volume: 3 start-page: 3431 year: 2013 ident: bib0006 article-title: Measuring memory with the order of fractional derivative publication-title: Sci Rep – start-page: 1 year: 2019 end-page: 11 ident: bib0029 article-title: Command filter-based adaptive NN control for MIMO nonlinear systems with full-state constraints and actuator hysteresis publication-title: IEEE Trans Fuzzy Syst – volume: 131 start-page: 1111 year: 2015 end-page: 1123 ident: bib0018 article-title: Large amplitude vibration of fractionally damped viscoelastic CNTs/fiber/polymer multiscale composite beams publication-title: Compos Struct – volume: 336 start-page: 454 year: 2018 end-page: 464 ident: bib0031 article-title: Numerical solutions of nonlinear fractional differential equations by alternative Legendre polynomials publication-title: Appl Math Comput – volume: 255 start-page: 1533 year: 2007 end-page: 1552 ident: bib0048 article-title: Finite difference/spectral approximations for the time-fractional diffusion equation publication-title: J Comput Phys – volume: 25 start-page: 92 year: 1938 end-page: 96 ident: bib0007 article-title: On fractional differences publication-title: Phil Mag – volume: 10 start-page: 1041 year: 2016 end-page: 1048 ident: bib0039 article-title: A new method for higher-order linear phase FIR digital filter using shifted chebyshev polynomials publication-title: Signal Image Video Process – volume: 16 start-page: 543 year: 2010 end-page: 552 ident: bib0002 article-title: A variable order constitutive relation for viscoelasticity publication-title: Ann Phys – volume: 50 start-page: 3505 year: 2013 end-page: 3510 ident: bib0017 article-title: Fractional visco-elastic euler bernoulli beam[j] publication-title: Int J Solids Struct – volume: 96 start-page: 317 year: 2018 end-page: 336 ident: bib0035 article-title: Numerical solutions for systems of fractional order differential equations with bernoulli wavelets publication-title: Int J Comput Math – volume: 244 start-page: 847 year: 2014 end-page: 858 ident: bib0032 article-title: Numerical solution of fractional partial differential equations with variable coefficients using generalized fractional-order legendre functions publication-title: Appl Math Comput – volume: 36 start-page: 1305 year: 2008 end-page: 1314 ident: bib0005 article-title: Nonlinear dynamics and chaos in a fractional-order financial system[j] publication-title: Chaos Solitons and Fractals – volume: 238 start-page: 329 year: 2014 end-page: 341 ident: bib0037 article-title: Numerical solution for the variable order linear cable equation with Bernstein polynomials publication-title: Appl Math Comput – volume: 339 start-page: 228 year: 2017 end-page: 243 ident: bib0013 article-title: Nonlinear vibration of viscoelastic beams described using fractional order derivatives publication-title: J Sound Vib – volume: 426 start-page: 258 year: 2018 end-page: 277 ident: bib0044 article-title: A modified variational method for nonlinear vibration analysis of rotating beams including coriolis effects publication-title: J Sound Vib – volume: 121 start-page: 10 year: 2013 end-page: 21 ident: bib0009 article-title: Steady state response of fractionally damped nonlinear viscoelastic arches by residue harmonic homotopy publication-title: Comput Struct – start-page: 20 year: 2015 end-page: 28 ident: bib0011 article-title: A fractional nonlinear creep model for coal considering damage effect and experimental validation publication-title: Int J Non-Linear Mech – volume: 34 start-page: 1482 year: 2010 end-page: 1497 ident: bib0021 article-title: Vibration and stability of an axially moving rayleigh beam publication-title: Appl Math Model – volume: 83 start-page: 133 year: 2014 end-page: 145 ident: bib0020 article-title: On the transient response of viscoelastic beams and plates on viscoelastic medium publication-title: Int J Mech Sci – volume: 11 start-page: 337 year: 2000 end-page: 344 ident: bib0026 article-title: Identification and prediction of discrete chaotic maps applying a Chebyshev neural network publication-title: Chaos Solitons Fractals – volume: 370 start-page: 114 year: 2006 end-page: 118 ident: bib0004 article-title: Coupled continuous time random walks in finance publication-title: Phys A Stat Mech Appl – volume: 85 start-page: 131 year: 2014 end-page: 147 ident: bib0023 article-title: Linear dynamical analysis of fractionally damped beams and rods publication-title: J Eng Math – volume: 200 start-page: 1466 year: 2015 end-page: 1482 ident: bib0040 article-title: Sensitivity analysis of a seismic risk scenario using sparse Chebyshev polynomial expansion publication-title: Geophys J Int – volume: 30 start-page: 3001 year: 2016 end-page: 3008 ident: bib0024 article-title: Application of radial basis functions and sinc method for solving the forced vibration of fractional viscoelastic beam publication-title: J Mech Sci Technol – volume: 7 start-page: 271 year: 2016 end-page: 283 ident: bib0001 article-title: Numerical study for multi-strain tuberculosis (TB) model of variable-order fractional derivatives publication-title: J Adv Res – start-page: 1235 year: 2016 end-page: 1241 ident: bib0036 article-title: Numerical study of a class of variable order nonlinear fractional differential equation in terms of bernstein polynomials publication-title: Ain Shams Eng J – volume: 30 start-page: 133 year: 1986 end-page: 155 ident: bib0008 article-title: On the fractional calculus model of viscoelasticity behavior publication-title: J Rheol – volume: 69 start-page: 2173 year: 2007 end-page: 2195 ident: bib0015 article-title: Finite element formulations for transient dynamic analysis in structural systems with viscoelastic treatments containing fractional derivative models publication-title: Int J Numer Methods Eng – volume: 56 start-page: 1591 year: 2017 end-page: 1602 ident: bib0041 article-title: Temporal phase unwrapping for fringe projection profilometry aided by recursion of Chebyshev polynomials publication-title: Appl Opt – volume: 90 start-page: 359 year: 2013 end-page: 378 ident: bib0034 article-title: Numerical solution of nonlinear fractional integral differential equations by using the second kind Chebyshev wavelets publication-title: Comput Model Eng Sci – volume: 73 start-page: 1377 year: 2017 end-page: 1384 ident: bib0047 article-title: Creep constitutive models for viscoelastic materials based on fractional derivatives publication-title: Comput Math Appl – volume: 330 start-page: 923 year: 2011 end-page: 936 ident: bib0010 article-title: Dynamic analysis of frames with viscoelastic dampers modelled by rheological models with fractional derivatives publication-title: J Sound Vib – volume: 35 start-page: 447 year: 2007 end-page: 553 ident: bib0003 article-title: Initialization, conceptualization, and application in the generalized (fractional) calculus publication-title: Crit Rev Biomed Eng – volume: 27 start-page: 1587 year: 2019 end-page: 1601 ident: bib0027 article-title: Adaptive fuzzy control for non-triangular structural stochastic switched nonlinear systems with full state constraints publication-title: IEEE Trans Fuzzy Syst – volume: 330 start-page: 923 issue: 5 year: 2011 ident: 10.1016/j.chaos.2019.109585_bib0010 article-title: Dynamic analysis of frames with viscoelastic dampers modelled by rheological models with fractional derivatives publication-title: J Sound Vib doi: 10.1016/j.jsv.2010.09.017 – volume: 61 start-page: 795 issue: 3 year: 2016 ident: 10.1016/j.chaos.2019.109585_bib0042 article-title: Analysing the stability of linear systems via exponential chebyshev polynomials publication-title: IEEE Trans Autom Control doi: 10.1109/TAC.2015.2449151 – volume: 131 start-page: 102 year: 2018 ident: 10.1016/j.chaos.2019.109585_bib0012 article-title: On the dynamics of non-local fractional viscoelastic beams under stochastic agencies publication-title: Compos B: Eng – volume: 71 start-page: 1365 issue: 11 year: 2007 ident: 10.1016/j.chaos.2019.109585_bib0022 article-title: Vibration analysis of beams with non-local foundations using the finite element method publication-title: Int J Numer Methods Eng doi: 10.1002/nme.2003 – volume: 30 start-page: 133 issue: 1 year: 1986 ident: 10.1016/j.chaos.2019.109585_bib0008 article-title: On the fractional calculus model of viscoelasticity behavior publication-title: J Rheol doi: 10.1122/1.549887 – volume: 14 start-page: 169 issue: 14 year: 2014 ident: 10.1016/j.chaos.2019.109585_bib0045 article-title: Effect of tapering on natural frequencies of rotating beams publication-title: Shock Vib – volume: 96 start-page: 317 issue: 2 year: 2018 ident: 10.1016/j.chaos.2019.109585_bib0035 article-title: Numerical solutions for systems of fractional order differential equations with bernoulli wavelets publication-title: Int J Comput Math doi: 10.1080/00207160.2018.1438604 – volume: 121 start-page: 10 issue: 5 year: 2013 ident: 10.1016/j.chaos.2019.109585_bib0009 article-title: Steady state response of fractionally damped nonlinear viscoelastic arches by residue harmonic homotopy publication-title: Comput Struct doi: 10.1016/j.compstruc.2013.02.011 – volume: 85 start-page: 131 issue: 1 year: 2014 ident: 10.1016/j.chaos.2019.109585_bib0023 article-title: Linear dynamical analysis of fractionally damped beams and rods publication-title: J Eng Math doi: 10.1007/s10665-013-9642-9 – volume: 21 start-page: 1506 issue: 6 year: 2018 ident: 10.1016/j.chaos.2019.109585_bib0038 article-title: Extrapolating for attaining high precision solutions for fractional partial differential equations[j] publication-title: Fract Calculus Appl Anal doi: 10.1515/fca-2018-0079 – start-page: 1235 year: 2016 ident: 10.1016/j.chaos.2019.109585_bib0036 article-title: Numerical study of a class of variable order nonlinear fractional differential equation in terms of bernstein polynomials publication-title: Ain Shams Eng J – volume: 90 start-page: 359 issue: 5 year: 2013 ident: 10.1016/j.chaos.2019.109585_bib0034 article-title: Numerical solution of nonlinear fractional integral differential equations by using the second kind Chebyshev wavelets publication-title: Comput Model Eng Sci – volume: 336 start-page: 454 year: 2018 ident: 10.1016/j.chaos.2019.109585_bib0031 article-title: Numerical solutions of nonlinear fractional differential equations by alternative Legendre polynomials publication-title: Appl Math Comput – volume: 50 start-page: 3505 issue: 22-23 year: 2013 ident: 10.1016/j.chaos.2019.109585_bib0017 article-title: Fractional visco-elastic euler bernoulli beam[j] publication-title: Int J Solids Struct doi: 10.1016/j.ijsolstr.2013.06.010 – volume: 155 start-page: 1 year: 2019 ident: 10.1016/j.chaos.2019.109585_bib0049 article-title: A fourier series solution for the transverse vibration of rotating beams with elastic boundary supports publication-title: Appl Acoust doi: 10.1016/j.apacoust.2019.05.008 – volume: 238 start-page: 329 issue: 7 year: 2014 ident: 10.1016/j.chaos.2019.109585_bib0037 article-title: Numerical solution for the variable order linear cable equation with Bernstein polynomials publication-title: Appl Math Comput – volume: 200 start-page: 1466 issue: 3 year: 2015 ident: 10.1016/j.chaos.2019.109585_bib0040 article-title: Sensitivity analysis of a seismic risk scenario using sparse Chebyshev polynomial expansion publication-title: Geophys J Int doi: 10.1093/gji/ggu491 – volume: 27 start-page: 1063 issue: 4 year: 2013 ident: 10.1016/j.chaos.2019.109585_bib0016 article-title: Large deflection of viscoelastic beams using fractional derivative model publication-title: J Eng Math – start-page: 20 issue: 76 year: 2015 ident: 10.1016/j.chaos.2019.109585_bib0011 article-title: A fractional nonlinear creep model for coal considering damage effect and experimental validation publication-title: Int J Non-Linear Mech doi: 10.1016/j.ijnonlinmec.2015.05.004 – volume: 16 start-page: 543 issue: 7-8 year: 2010 ident: 10.1016/j.chaos.2019.109585_bib0002 article-title: A variable order constitutive relation for viscoelasticity publication-title: Ann Phys doi: 10.1002/andp.200751907-803 – volume: 40 start-page: 7988 issue: 17 year: 2016 ident: 10.1016/j.chaos.2019.109585_bib0025 article-title: A modified variational iteration method for the analysis of viscoelastic beams publication-title: Appl Math Model doi: 10.1016/j.apm.2016.04.011 – volume: 56 start-page: 1591 issue: 6 year: 2017 ident: 10.1016/j.chaos.2019.109585_bib0041 article-title: Temporal phase unwrapping for fringe projection profilometry aided by recursion of Chebyshev polynomials publication-title: Appl Opt doi: 10.1364/AO.56.001591 – volume: 244 start-page: 847 issue: 2 year: 2014 ident: 10.1016/j.chaos.2019.109585_bib0032 article-title: Numerical solution of fractional partial differential equations with variable coefficients using generalized fractional-order legendre functions publication-title: Appl Math Comput – volume: 35 start-page: 447 issue: 6 year: 2007 ident: 10.1016/j.chaos.2019.109585_bib0003 article-title: Initialization, conceptualization, and application in the generalized (fractional) calculus publication-title: Crit Rev Biomed Eng doi: 10.1615/CritRevBiomedEng.v35.i6.10 – volume: 199 start-page: 366 year: 2017 ident: 10.1016/j.chaos.2019.109585_bib0019 article-title: Sensitivity analysis of dynamic characteristics of composite beams with viscoelastic layers publication-title: Proc Eng doi: 10.1016/j.proeng.2017.09.041 – volume: 298 start-page: 1034 issue: 4 year: 2006 ident: 10.1016/j.chaos.2019.109585_bib0046 article-title: Free vibration of rotating tapered beams using the dynamic stiffness method publication-title: J Sound Vib doi: 10.1016/j.jsv.2006.06.040 – volume: 85 start-page: 1793 issue: 12 year: 2015 ident: 10.1016/j.chaos.2019.109585_bib0014 article-title: Dynamic characteristics of multilayered beams with viscoelastic layers described by the fractional zener model publication-title: Arch Appl Mech doi: 10.1007/s00419-015-1019-2 – volume: 27 start-page: 2152 issue: 11 year: 2019 ident: 10.1016/j.chaos.2019.109585_bib0028 article-title: Observer-based fuzzy adaptive event-triggered control for pure-feedback nonlinear systems with prescribed performance publication-title: IEEE Trans Fuzzy Syst doi: 10.1109/TFUZZ.2019.2895560 – volume: 73 start-page: 1377 issue: 6 year: 2017 ident: 10.1016/j.chaos.2019.109585_bib0047 article-title: Creep constitutive models for viscoelastic materials based on fractional derivatives publication-title: Comput Math Appl doi: 10.1016/j.camwa.2016.05.002 – volume: 370 start-page: 114 issue: 1 year: 2006 ident: 10.1016/j.chaos.2019.109585_bib0004 article-title: Coupled continuous time random walks in finance publication-title: Phys A Stat Mech Appl doi: 10.1016/j.physa.2006.04.034 – volume: 10 start-page: 1041 issue: 6 year: 2016 ident: 10.1016/j.chaos.2019.109585_bib0039 article-title: A new method for higher-order linear phase FIR digital filter using shifted chebyshev polynomials publication-title: Signal Image Video Process doi: 10.1007/s11760-015-0856-3 – volume: 11 start-page: 337 issue: 1-3 year: 2000 ident: 10.1016/j.chaos.2019.109585_bib0026 article-title: Identification and prediction of discrete chaotic maps applying a Chebyshev neural network publication-title: Chaos Solitons Fractals doi: 10.1016/S0960-0779(98)00302-6 – volume: 69 start-page: 2173 issue: 10 year: 2007 ident: 10.1016/j.chaos.2019.109585_bib0015 article-title: Finite element formulations for transient dynamic analysis in structural systems with viscoelastic treatments containing fractional derivative models publication-title: Int J Numer Methods Eng doi: 10.1002/nme.1840 – volume: 25 start-page: 92 issue: 1 year: 1938 ident: 10.1016/j.chaos.2019.109585_bib0007 article-title: On fractional differences publication-title: Phil Mag – volume: 36 start-page: 1305 issue: 5 year: 2008 ident: 10.1016/j.chaos.2019.109585_bib0005 article-title: Nonlinear dynamics and chaos in a fractional-order financial system[j] publication-title: Chaos Solitons and Fractals doi: 10.1016/j.chaos.2006.07.051 – volume: 34 start-page: 1482 issue: 6 year: 2010 ident: 10.1016/j.chaos.2019.109585_bib0021 article-title: Vibration and stability of an axially moving rayleigh beam publication-title: Appl Math Model doi: 10.1016/j.apm.2009.08.022 – volume: 213 start-page: 205 issue: 1 year: 2006 ident: 10.1016/j.chaos.2019.109585_bib0030 article-title: A second-order accurate numerical approximation for the fractional diffusion equation publication-title: J Comput Phys doi: 10.1016/j.jcp.2005.08.008 – volume: 3 start-page: 3431 issue: 7478 year: 2013 ident: 10.1016/j.chaos.2019.109585_bib0006 article-title: Measuring memory with the order of fractional derivative publication-title: Sci Rep doi: 10.1038/srep03431 – volume: 83 start-page: 133 issue: 7-8 year: 2014 ident: 10.1016/j.chaos.2019.109585_bib0020 article-title: On the transient response of viscoelastic beams and plates on viscoelastic medium publication-title: Int J Mech Sci doi: 10.1016/j.ijmecsci.2014.03.007 – start-page: 1 year: 2019 ident: 10.1016/j.chaos.2019.109585_bib0029 article-title: Command filter-based adaptive NN control for MIMO nonlinear systems with full-state constraints and actuator hysteresis publication-title: IEEE Trans Fuzzy Syst – volume: 142-143 start-page: 440 year: 2018 ident: 10.1016/j.chaos.2019.109585_bib0043 article-title: Non-rotating beams isospectral to rotating rayleigh beams publication-title: Int J Mech Sci doi: 10.1016/j.ijmecsci.2018.04.049 – volume: 30 start-page: 3001 issue: 7 year: 2016 ident: 10.1016/j.chaos.2019.109585_bib0024 article-title: Application of radial basis functions and sinc method for solving the forced vibration of fractional viscoelastic beam publication-title: J Mech Sci Technol doi: 10.1007/s12206-016-0306-3 – volume: 339 start-page: 228 issue: 2 year: 2017 ident: 10.1016/j.chaos.2019.109585_bib0013 article-title: Nonlinear vibration of viscoelastic beams described using fractional order derivatives publication-title: J Sound Vib doi: 10.1016/j.jsv.2017.03.032 – volume: 131 start-page: 1111 year: 2015 ident: 10.1016/j.chaos.2019.109585_bib0018 article-title: Large amplitude vibration of fractionally damped viscoelastic CNTs/fiber/polymer multiscale composite beams publication-title: Compos Struct doi: 10.1016/j.compstruct.2015.06.038 – volume: 27 start-page: 1587 issue: 8 year: 2019 ident: 10.1016/j.chaos.2019.109585_bib0027 article-title: Adaptive fuzzy control for non-triangular structural stochastic switched nonlinear systems with full state constraints publication-title: IEEE Trans Fuzzy Syst doi: 10.1109/TFUZZ.2018.2883374 – volume: 255 start-page: 1533 issue: 2 year: 2007 ident: 10.1016/j.chaos.2019.109585_bib0048 article-title: Finite difference/spectral approximations for the time-fractional diffusion equation publication-title: J Comput Phys doi: 10.1016/j.jcp.2007.02.001 – volume: 332 start-page: 197 year: 2018 ident: 10.1016/j.chaos.2019.109585_bib0033 article-title: A two-dimensional Chebyshev wavelets approach for solving the Fokker–Planck equations of time and space fractional derivatives type with variable coefficients publication-title: Appl Math Comput – volume: 426 start-page: 258 year: 2018 ident: 10.1016/j.chaos.2019.109585_bib0044 article-title: A modified variational method for nonlinear vibration analysis of rotating beams including coriolis effects publication-title: J Sound Vib doi: 10.1016/j.jsv.2018.04.027 – volume: 7 start-page: 271 issue: 2 year: 2016 ident: 10.1016/j.chaos.2019.109585_bib0001 article-title: Numerical study for multi-strain tuberculosis (TB) model of variable-order fractional derivatives publication-title: J Adv Res doi: 10.1016/j.jare.2015.06.004 |
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| SubjectTerms | Approximation technique Fractional governing equation Fractional visco-elastic rotating beam Mathematics Numerical solution Operator matrix Shifted Chebyshev polynomials |
| Title | Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam |
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