메뉴 건너뛰기




Volumn 49, Issue , 2013, Pages 159-169

Solution of the model of beam-type micro- and nano-scale electrostatic actuators by a new modified Adomian decomposition method for nonlinear boundary value problems

Author keywords

Adomian decomposition method; Casimir force; Micro electromechanical systems (MEMS); Nano electromechanical systems (NEMS); Nonlinear boundary value problems; Van der Waals force

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; CONTROL EQUIPMENT; DIFFERENTIAL EQUATIONS; ELECTROSTATIC ACTUATORS; INTEGRAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS; MEMS; NANOCANTILEVERS; NANOTECHNOLOGY; NEMS; NONLINEAR EQUATIONS; QUANTUM THEORY; VAN DER WAALS FORCES;

EID: 84869865497     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2012.10.003     Document Type: Article
Times cited : (68)

References (59)
  • 2
    • 27144514757 scopus 로고    scopus 로고
    • Adomian decomposition method used for solving nonlinear pull-in behavior in electrostatic micro-actuators
    • J.H. Kuang, C.J. Chen, Adomian decomposition method used for solving nonlinear pull-in behavior in electrostatic micro-actuators, Mathematical and Computer Modelling 41 (2005) 1479-1491.
    • (2005) Mathematical and Computer Modelling , vol.41 , pp. 1479-1491
    • Kuang, J.H.1    Chen, C.J.2
  • 5
    • 84866250117 scopus 로고    scopus 로고
    • Efficiency of modified Adomian decomposition for simulating the instability of nano-electromechanical switches: Comparison with the conventional decomposition method
    • A. Koochi, M. Abadyan, Efficiency of modified Adomian decomposition for simulating the instability of nano-electromechanical switches: comparison with the conventional decomposition method, Trends in Applied Sciences Research 7 (2012) 57-67.
    • (2012) Trends in Applied Sciences Research , vol.7 , pp. 57-67
    • Koochi, A.1    Abadyan, M.2
  • 6
    • 34047148779 scopus 로고    scopus 로고
    • Closed-form solutions of the pull-in instability in nano-cantilevers under electrostatic and intermolecular surface forces
    • DOI 10.1016/j.ijsolstr.2006.12.015, PII S0020768306005403
    • A. Ramezani, A. Alasty, J. Akbari, Closed-form solutions of the pull-in instability in nano-cantilevers under electrostatic and intermolecular surface forces, International Journal of Solids and Structures 44 (2007) 4925-4941. (Pubitemid 46509506)
    • (2007) International Journal of Solids and Structures , vol.44 , Issue.14-15 , pp. 4925-4941
    • Ramezani, A.1    Alasty, A.2    Akbari, J.3
  • 8
    • 12544250636 scopus 로고    scopus 로고
    • The casimir force: Background, experiments, and applications
    • S.K. Lamoreaux, The Casimir force: background, experiments, and applications, Reports on Progress in Physics 68 (2005) 201-236.
    • (2005) Reports on Progress in Physics , vol.68 , pp. 201-236
    • Lamoreaux, S.K.1
  • 9
    • 78649633873 scopus 로고    scopus 로고
    • Theoretical study of the effect of Casimir attraction on the pull-in behavior of beam-type NEMS using modified Adomian method
    • A. Koochi, A.S. Kazemi, Y.T. Beni, A. Yekrangi, M. Abadyan, Theoretical study of the effect of Casimir attraction on the pull-in behavior of beam-type NEMS using modified Adomian method, Physica E 43 (2010) 625-632.
    • (2010) Physica e , vol.43 , pp. 625-632
    • Koochi, A.1    Kazemi, A.S.2    Beni, Y.T.3    Yekrangi, A.4    Abadyan, M.5
  • 10
    • 9544220680 scopus 로고    scopus 로고
    • Nonlinear behavior for nanoscale electrostatic actuators with Casimir force, Chaos
    • W.H. Lin, Y.P. Zhao, Nonlinear behavior for nanoscale electrostatic actuators with Casimir force, Chaos, Solitons and Fractals 23 (2005) 1777-1785.
    • (2005) Solitons and Fractals , vol.23 , pp. 1777-1785
    • Lin, W.H.1    Zhao, Y.P.2
  • 12
    • 80052946303 scopus 로고    scopus 로고
    • Investigation of elastic boundary condition on the pull-in instability of beam-type NEMS under van der Waals attraction
    • M.R. Abadyana, Y.T. Beni, A. Noghrehabadi, Investigation of elastic boundary condition on the pull-in instability of beam-type NEMS under van der Waals attraction, Procedia Engineering 10 (2011) 1724-1729.
    • (2011) Procedia Engineering , vol.10 , pp. 1724-1729
    • Abadyana, M.R.1    Beni, Y.T.2    Noghrehabadi, A.3
  • 13
    • 84867333638 scopus 로고    scopus 로고
    • A new approach to the electrostatic pull-in instability of nanocantilever actuators using the ADM-Padé technique
    • A. Noghrehabadi, M. Ghalambaz, A. Ghanbarzadeh, A new approach to the electrostatic pull-in instability of nanocantilever actuators using the ADM-Padé technique, Computers & Mathematics with Applications 64 (2012) 2806-2815.
    • (2012) Computers & Mathematics with Applications , vol.64 , pp. 2806-2815
    • Noghrehabadi, A.1    Ghalambaz, M.2    Ghanbarzadeh, A.3
  • 14
    • 78149363758 scopus 로고    scopus 로고
    • Investigating the effect of Casimir and van der Waals attractions on the electrostatic pull-in instability of nano-actuators
    • 045801
    • R. Soroush, A. Koochi, A.S. Kazemi, A. Noghrehabadi, H. Haddadpour, M. Abadyan, Investigating the effect of Casimir and van der Waals attractions on the electrostatic pull-in instability of nano-actuators, Physica Scripta 82 (2010) 045801. (11pp).
    • (2010) Physica Scripta , vol.82 , pp. 11
    • Soroush, R.1    Koochi, A.2    Kazemi, A.S.3    Noghrehabadi, A.4    Haddadpour, H.5    Abadyan, M.6
  • 15
    • 84879886314 scopus 로고    scopus 로고
    • Modeling effects of three nano-scale physical phenomena on instability voltage of multi-layer MEMS/NEMS: Material size dependency, van der Waals force and non-classic support conditions
    • A.Y. Salekdeh, A. Koochi, Y.T. Beni, M. Abadyan, Modeling effects of three nano-scale physical phenomena on instability voltage of multi-layer MEMS/NEMS: Material size dependency, van der Waals force and non-classic support conditions, Trends in Applied Sciences Research 7 (2012) 1-17.
    • (2012) Trends in Applied Sciences Research , vol.7 , pp. 1-17
    • Salekdeh, A.Y.1    Koochi, A.2    Beni, Y.T.3    Abadyan, M.4
  • 16
    • 79551521851 scopus 로고    scopus 로고
    • Theoretical study of the effect of Casimir force, elastic boundary conditions and size dependency on the pull-in instability of beam-type NEMS
    • Y.T. Beni, A. Koochi, M. Abadyan, Theoretical study of the effect of Casimir force, elastic boundary conditions and size dependency on the pull-in instability of beam-type NEMS, Physica E 43 (2011) 979-988.
    • (2011) Physica e , vol.43 , pp. 979-988
    • Beni, Y.T.1    Koochi, A.2    Abadyan, M.3
  • 17
    • 81855213077 scopus 로고    scopus 로고
    • A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations
    • J.S. Duan, R. Rach, A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations, Applied Mathematics and Computation 218 (2011) 4090-4118.
    • (2011) Applied Mathematics and Computation , vol.218 , pp. 4090-4118
    • Duan, J.S.1    Rach, R.2
  • 22
    • 0008485419 scopus 로고
    • An efficient methodology for the physical sciences
    • G. Adomian, R. Rach, R. Meyers, An efficient methodology for the physical sciences, Kybernetes 20 (1991) 24-34.
    • (1991) Kybernetes , vol.20 , pp. 24-34
    • Adomian, G.1    Rach, R.2    Meyers, R.3
  • 25
    • 51349098347 scopus 로고    scopus 로고
    • A new definition of the Adomian polynomials
    • R. Rach, A new definition of the Adomian polynomials, Kybernetes 37 (2008) 910-955.
    • (2008) Kybernetes , vol.37 , pp. 910-955
    • Rach, R.1
  • 30
    • 34548650489 scopus 로고    scopus 로고
    • Approximate analytical solutions for models of three-dimensional electrodes by Adomian's decomposition method
    • in: C.G. Vaye-nas, R.E. White, M.E. Gamboa-Adelco (Eds.), Springer, New York
    • K. Scott, Y.P. Sun, Approximate analytical solutions for models of three-dimensional electrodes by Adomian's decomposition method, in: C.G. Vaye-nas, R.E. White, M.E. Gamboa-Adelco (Eds.), Modern Aspects of Electrochemistry, vol. 41, Springer, New York, 2007, pp. 222-304.
    • (2007) Modern Aspects of Electrochemistry , vol.41 , pp. 222-304
    • Scott, K.1    Sun, Y.P.2
  • 33
    • 77952177749 scopus 로고    scopus 로고
    • Finding approximate solutions for a class of third-order non-linear boundary value problems via the decomposition method of Adomian
    • M. Dehghan, M. Tatari, Finding approximate solutions for a class of third-order non-linear boundary value problems via the decomposition method of Adomian, International Journal of Computer Mathematics 87 (2010) 1256-1263.
    • (2010) International Journal of Computer Mathematics , vol.87 , pp. 1256-1263
    • Dehghan, M.1    Tatari, M.2
  • 34
    • 33750433241 scopus 로고    scopus 로고
    • An adaptation of adomian decomposition for numeric-analytic integration of strongly nonlinear and chaotic oscillators
    • DOI 10.1016/j.cma.2006.08.010, PII S0045782506002520
    • S. Ghosh, A. Roy, D. Roy, An adaptation of Adomian decomposition for numeric-analytic integration of strongly nonlinear and chaotic oscillators, Computer Methods in Applied Mechanics and Engineering 196 (2007) 1133-1153. (Pubitemid 44644881)
    • (2007) Computer Methods in Applied Mechanics and Engineering , vol.196 , Issue.4-6 , pp. 1133-1153
    • Ghosh, S.1    Roy, A.2    Roy, D.3
  • 35
    • 34648844213 scopus 로고    scopus 로고
    • Numeric-analytic form of the adomian decomposition method for two-point boundary value problems in nonlinear mechanics
    • DOI 10.1061/(ASCE)0733-9399(2007)133:10(1124)
    • S. Ghosh, D. Roy, Numeric-analytic form of the Adomian decomposition method for two-point boundary value problems in nonlinear mechanics, Journal of Engineering Mechanics 133 (2007) 1124-1133. (Pubitemid 47456363)
    • (2007) Journal of Engineering Mechanics , vol.133 , Issue.10 , pp. 1124-1133
    • Ghosh, S.1    Roy, D.2
  • 36
    • 80053279824 scopus 로고    scopus 로고
    • New higher-order numerical one-step methods based on the Adomian and the modified decomposition methods
    • J.S. Duan, R. Rach, New higher-order numerical one-step methods based on the Adomian and the modified decomposition methods, Applied Mathematics and Computation 218 (2011) 2810-2828.
    • (2011) Applied Mathematics and Computation , vol.218 , pp. 2810-2828
    • Duan, J.S.1    Rach, R.2
  • 37
    • 84980392608 scopus 로고    scopus 로고
    • A bibliography of the theory and applications of the Adomian decomposition method, 1961-2011
    • R. Rach, A bibliography of the theory and applications of the Adomian decomposition method, 1961-2011, Kybernetes 41 (2012) 1087-1148.
    • (2012) Kybernetes , vol.41 , pp. 1087-1148
    • Rach, R.1
  • 38
    • 84874054174 scopus 로고    scopus 로고
    • A review of the Adomian decomposition method and its applications to fractional differential equations
    • J.S. Duan, R. Rach, D. Baleanu, A.M. Wazwaz, A review of the Adomian decomposition method and its applications to fractional differential equations, Communications in Fractional Calculus 3 (2012) 73-99.
    • (2012) Communications in Fractional Calculus , vol.3 , pp. 73-99
    • Duan, J.S.1    Rach, R.2    Baleanu, D.3    Wazwaz, A.M.4
  • 39
    • 0021500393 scopus 로고
    • Convenient computational form for the adomian polynomials
    • R. Rach, A convenient computational form for the Adomian polynomials, Journal of Mathematical Analysis and Applications 102 (1984) 415-419. (Pubitemid 14663530)
    • (1984) Journal of Mathematical Analysis and Applications , vol.102 , Issue.2 , pp. 415-419
    • Rach, R.1
  • 40
    • 0347450513 scopus 로고    scopus 로고
    • A new algorithm for calculating Adomian polynomials for nonlinear operators
    • A.M. Wazwaz, A new algorithm for calculating Adomian polynomials for nonlinear operators, Applied Mathematics and Computation 111 (2000) 53-69.
    • (2000) Applied Mathematics and Computation , vol.111 , pp. 53-69
    • Wazwaz, A.M.1
  • 41
    • 0037420925 scopus 로고    scopus 로고
    • A mathematical model of Adomian polynomials
    • F. Abdelwahid, A mathematical model of Adomian polynomials, Applied Mathematics and Computation 141 (2003) 447-453.
    • (2003) Applied Mathematics and Computation , vol.141 , pp. 447-453
    • Abdelwahid, F.1
  • 42
    • 32144435938 scopus 로고    scopus 로고
    • An improvement to an alternate algorithm for computing Adomian polynomials in special cases
    • DOI 10.1016/j.amc.2005.04.052, PII S0096300305003772
    • J. Biazar, M. Ilie, A. Khoshkenar, An improvement to an alternate algorithm for computing Adomian polynomials in special cases, Applied Mathematics and Computation 173 (2006) 582-592. (Pubitemid 43208800)
    • (2006) Applied Mathematics and Computation , vol.173 , Issue.1 , pp. 582-592
    • Biazar, J.1    Ilie, M.2    Khoshkenar, A.3
  • 43
    • 27144469470 scopus 로고    scopus 로고
    • A new algorithm for calculating Adomian polynomials
    • DOI 10.1016/j.amc.2004.09.082, PII S0096300304007829
    • Y. Zhu, Q. Chang, S. Wu, A new algorithm for calculating Adomian polynomials, Applied Mathematics and Computation 169 (2005) 402-416. (Pubitemid 41491862)
    • (2005) Applied Mathematics and Computation , vol.169 , Issue.1 , pp. 402-416
    • Zhu, Y.1    Chang, Q.2    Wu, S.3
  • 45
    • 77949913663 scopus 로고    scopus 로고
    • Recurrence triangle for Adomian polynomials
    • J.S. Duan, Recurrence triangle for Adomian polynomials, Applied Mathematics and Computation 216 (2010) 1235-1241.
    • (2010) Applied Mathematics and Computation , vol.216 , pp. 1235-1241
    • Duan, J.S.1
  • 46
    • 77958013614 scopus 로고    scopus 로고
    • An efficient algorithm for the multivariable Adomian polynomials
    • J.S. Duan, An efficient algorithm for the multivariable Adomian polynomials, Applied Mathematics and Computation 217 (2010) 2456-2467.
    • (2010) Applied Mathematics and Computation , vol.217 , pp. 2456-2467
    • Duan, J.S.1
  • 47
    • 79952005459 scopus 로고    scopus 로고
    • Convenient analytic recurrence algorithms for the Adomian polynomials
    • J.S. Duan, Convenient analytic recurrence algorithms for the Adomian polynomials, Applied Mathematics and Computation 217 (2011) 6337-6348.
    • (2011) Applied Mathematics and Computation , vol.217 , pp. 6337-6348
    • Duan, J.S.1
  • 48
    • 77956114544 scopus 로고    scopus 로고
    • Reduced polynomials and their generation in Adomian decomposition methods
    • J.S. Duan, A.P. Guo, Reduced polynomials and their generation in Adomian decomposition methods, CMES-Computer Modeling in Engineering & Sciences 60 (2010) 139-150.
    • (2010) CMES-Computer Modeling in Engineering & Sciences , vol.60 , pp. 139-150
    • Duan, J.S.1    Guo, A.P.2
  • 49
    • 80053367331 scopus 로고    scopus 로고
    • New recurrence algorithms for the nonclassic Adomian polynomials
    • J.S. Duan, New recurrence algorithms for the nonclassic Adomian polynomials, Computers & Mathematics with Applications 62 (2011) 2961-2977.
    • (2011) Computers & Mathematics with Applications , vol.62 , pp. 2961-2977
    • Duan, J.S.1
  • 50
    • 84859426693 scopus 로고    scopus 로고
    • Symbolic implementation of a new, fast algorithm for the multivariable Adomian polynomials
    • IEEE, Beijing
    • J.S. Duan, A.P. Guo, Symbolic implementation of a new, fast algorithm for the multivariable Adomian polynomials, in: Proceedings 2011 World Congress on Engineering and Technology, vol. 1, IEEE, Beijing, 2011, pp. 72-74.
    • (2011) Proceedings 2011 World Congress on Engineering and Technology , vol.1 , pp. 72-74
    • Duan, J.S.1    Guo, A.P.2
  • 51
    • 0022756945 scopus 로고
    • Noisy convergence phenomena in decomposition method solutions
    • DOI 10.1016/0377-0427(86)90228-1
    • G. Adomian, R. Rach, The noisy convergence phenomena in decomposition method solutions, Journal of Computational and Applied Mathematics 15 (1986) 379-381. (Pubitemid 16640498)
    • (1986) Journal of Computational and Applied Mathematics , vol.15 , Issue.3 , pp. 379-381
    • Adomian, G.1    Rach, R.2
  • 53
    • 0040313517 scopus 로고    scopus 로고
    • A reliable modification of Adomian decomposition method
    • A.M. Wazwaz, A reliable modification of Adomian decomposition method, Applied Mathematics and Computation 102 (1999) 77-86.
    • (1999) Applied Mathematics and Computation , vol.102 , pp. 77-86
    • Wazwaz, A.M.1
  • 54
    • 0035882676 scopus 로고    scopus 로고
    • A new modification of the Adomian decomposition method for linear and nonlinear operators
    • DOI 10.1016/S0096-3003(00)00060-6, PII S0096300300000606
    • A.M. Wazwaz, S.M. El-Sayed, A new modification of the Adomian decomposition method for linear and nonlinear operators, Applied Mathematics and Computation 122 (2001) 393-405. (Pubitemid 32645602)
    • (2001) Applied Mathematics and Computation , vol.122 , Issue.3 , pp. 393-405
    • Wazwaz, A.-M.1    El-Sayed, S.M.2
  • 55
    • 0000004102 scopus 로고
    • Analytic solution of nonlinear boundary-value problems in several dimensions by decomposition
    • G. Adomian, R. Rach, Analytic solution of nonlinear boundary-value problems in several dimensions by decomposition, Journal of Mathematical Analysis and Applications 174 (1993) 118-137.
    • (1993) Journal of Mathematical Analysis and Applications , vol.174 , pp. 118-137
    • Adomian, G.1    Rach, R.2
  • 56
    • 39049159649 scopus 로고
    • A new algorithm for matching boundary conditions in decomposition solutions
    • G. Adomian, R. Rach, A new algorithm for matching boundary conditions in decomposition solutions, Applied Mathematics and Computation 58 (1993) 61-68.
    • (1993) Applied Mathematics and Computation , vol.58 , pp. 61-68
    • Adomian, G.1    Rach, R.2
  • 57
    • 33751540614 scopus 로고
    • Modified decomposition solution of linear and nonlinear boundary-value problems
    • G. Adomian, R. Rach, Modified decomposition solution of linear and nonlinear boundary-value problems, Nonlinear Analysis 23 (1994) 615-619.
    • (1994) Nonlinear Analysis , vol.23 , pp. 615-619
    • Adomian, G.1    Rach, R.2
  • 58
  • 59
    • 0022184556 scopus 로고
    • Nonlinear differential equations with negative power nonlinearities
    • DOI 10.1016/0022-247X(85)90258-6
    • G. Adomian, R. Rach, Nonlinear differential equations with negative power nonlinearities, Journal of Mathematical Analysis and Applications 112 (1985) 497-501. (Pubitemid 16507890)
    • (1985) Journal of Mathematical Analysis and Applications , vol.112 , Issue.2 , pp. 497-501
    • Adomian, G.1    Rach, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.