메뉴 건너뛰기




Volumn 72, Issue 3, 2013, Pages 671-682

A comparison of stability computational methods for periodic solution of nonlinear problems with application to rotordynamics

Author keywords

Floquet theory; Harmonic Balance Method; Rotor nonlinear dynamics; Rotor stator contact; Stability

Indexed keywords

COMPARATIVE STUDIES; FLOQUET THEORY; HARMONIC BALANCE METHOD; NONLINEAR PROBLEMS; PERIODIC SOLUTION; ROTOR-DYNAMICS; VARIABLE NUMBER;

EID: 84880702302     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-012-0744-0     Document Type: Article
Times cited : (81)

References (33)
  • 1
    • 0032117342 scopus 로고    scopus 로고
    • An algorithm for response and stability of large order non-linear systems - Application to rotor systems
    • 10.1006/jsvi.1998.1614 10.1006/jsvi.1998.1614
    • Sundararajan, P.; Noah, S.T.: An algorithm for response and stability of large order non-linear systems - application to rotor systems. J. Sound Vib. 214(4), 695-723 (1998). doi: 10.1006/jsvi.1998.1614
    • (1998) J. Sound Vib. , vol.214 , Issue.4 , pp. 695-723
    • Sundararajan, P.1    Noah, S.T.2
  • 2
    • 0024641167 scopus 로고
    • Periodic solutions in rotor dynamic systems with nonlinear supports: A general approach
    • 10.1115/1.3269840 10.1115/1.3269840
    • Nataraj, C.; Nelson, H.D.: Periodic solutions in rotor dynamic systems with nonlinear supports: a general approach. J. Vib. Acoust. 111(2), 187-193 (1989). doi: 10.1115/1.3269840
    • (1989) J. Vib. Acoust. , vol.111 , Issue.2 , pp. 187-193
    • Nataraj, C.1    Nelson, H.D.2
  • 3
    • 0035932216 scopus 로고    scopus 로고
    • The harmonic balance method with arc-length continuation in rotor/stator contact problems
    • 10.1006/jsvi.2000.3298 10.1006/jsvi.2000.3298
    • Von Groll, G.; Ewins, D.J.: The harmonic balance method with arc-length continuation in rotor/stator contact problems. J. Sound Vib. 241(2), 223-233 (2001). doi: 10.1006/jsvi.2000.3298
    • (2001) J. Sound Vib. , vol.241 , Issue.2 , pp. 223-233
    • Von Groll, G.1    Ewins, D.J.2
  • 4
    • 0017441527 scopus 로고
    • Efficient numerical treatment of periodic systems with application to stability problems
    • 10.1002/nme.1620110708 472183 0367.73059 10.1002/nme.1620110708
    • Friedmann, P.; Hammond, C.E.; Woo, T.H.: Efficient numerical treatment of periodic systems with application to stability problems. Int. J. Numer. Methods Eng. 11(7), 1117-1136 (1977). doi: 10.1002/nme.1620110708
    • (1977) Int. J. Numer. Methods Eng. , vol.11 , Issue.7 , pp. 1117-1136
    • Friedmann, P.1    Hammond, C.E.2    Woo, T.H.3
  • 5
    • 0022436533 scopus 로고
    • Numerical methods for determining the stability and response of periodic systems with applications to helicopter rotor dynamics and aeroelasticity
    • 10.1016/0898-1221(86)90091-X 10.1016/0898-1221(86)90091-X
    • Friedmann, P.: Numerical methods for determining the stability and response of periodic systems with applications to helicopter rotor dynamics and aeroelasticity. Comput. Math. Appl. 12(1, Part A), 131-148 (1986). doi: 10.1016/0898-1221(86)90091-X
    • (1986) Comput. Math. Appl. , vol.12 , Issue.1 PART A , pp. 131-148
    • Friedmann, P.1
  • 6
    • 0019590967 scopus 로고
    • On computing Floquet transition matrices of rotorcraft
    • 10.4050/JAHS.26.56 10.4050/JAHS.26.56
    • Gaonkar, G.H.; Simha Prasad, D.S.; Sastry, D.: On computing Floquet transition matrices of rotorcraft. J. Am. Helicopter Soc. 26(3), 56-61 (1981). doi: 10.4050/JAHS.26.56
    • (1981) J. Am. Helicopter Soc. , vol.26 , Issue.3 , pp. 56-61
    • Gaonkar, G.H.1    Simha Prasad, D.S.2    Sastry, D.3
  • 7
    • 0026260006 scopus 로고
    • An efficient computational scheme for the analysis of periodic systems
    • 10.1016/0022-460X(91)90654-3 1139953 10.1016/0022-460X(91)90654-3
    • Sinha, S.; Wu, D.H.: An efficient computational scheme for the analysis of periodic systems. J. Sound Vib. 151(1), 91-117 (1991). doi: 10.1016/0022-460X(91)90654-3
    • (1991) J. Sound Vib. , vol.151 , Issue.1 , pp. 91-117
    • Sinha, S.1    Wu, D.H.2
  • 8
    • 84880701470 scopus 로고
    • A new approach in the analysis of linear systems with periodic coefficients for applications in rotorcraft dynamics
    • Wu, D.H.; Sinha, S.: A new approach in the analysis of linear systems with periodic coefficients for applications in rotorcraft dynamics. J. R. Aeronaut. Soc. 1, 8-16 (1994)
    • (1994) J. R. Aeronaut. Soc. , vol.1 , pp. 8-16
    • Wu, D.H.1    Sinha, S.2
  • 9
    • 0027641287 scopus 로고
    • Dynamic stability and chaos of system with piecewise linear stiffness
    • 10.1061/(ASCE)0733-9399(1993)119:8(1542)
    • Liaw, C.Y.; Koh, C.G.: Dynamic stability and chaos of system with piecewise linear stiffness. J. Eng. Mech. 119, 1542-1558 (1993)
    • (1993) J. Eng. Mech. , vol.119 , pp. 1542-1558
    • Liaw, C.Y.1    Koh, C.G.2
  • 10
    • 0000718955 scopus 로고    scopus 로고
    • Bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method
    • 10.1006/jsvi.1999.2264 10.1006/jsvi.1999.2264
    • Raghothama, A.; Narayanan, S.: Bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method. J. Sound Vib. 226(3), 469-492 (1999). doi: 10.1006/jsvi.1999.2264
    • (1999) J. Sound Vib. , vol.226 , Issue.3 , pp. 469-492
    • Raghothama, A.1    Narayanan, S.2
  • 11
    • 0032658183 scopus 로고    scopus 로고
    • An efficient analysis of high-order dynamical system with local nonlinearity
    • 10.1115/1.2893995 10.1115/1.2893995
    • Zheng, T.; Hasebe, N.: An efficient analysis of high-order dynamical system with local nonlinearity. J. Vib. Acoust. 121(3), 408-416 (1999). doi: 10.1115/1.2893995
    • (1999) J. Vib. Acoust. , vol.121 , Issue.3 , pp. 408-416
    • Zheng, T.1    Hasebe, N.2
  • 12
    • 0030081113 scopus 로고    scopus 로고
    • Quasi-periodic response and stability analysis for a non-linear Jeffcott rotor
    • 10.1006/jsvi.1996.0059 10.1006/jsvi.1996.0059
    • Kim, Y.B.; Noah, S.T.: Quasi-periodic response and stability analysis for a non-linear Jeffcott rotor. J. Sound Vib. 190(2), 239-253 (1996). doi: 10.1006/jsvi.1996.0059
    • (1996) J. Sound Vib. , vol.190 , Issue.2 , pp. 239-253
    • Kim, Y.B.1    Noah, S.T.2
  • 13
    • 42449127128 scopus 로고    scopus 로고
    • Bifurcation and route-to-chaos analyses for Mathieu-duffing oscillator by the incremental harmonic balance method
    • 1170.70367 10.1007/s11071-007-9289-z
    • Shen, J.; Lin, K.; Chen, S.; Sze, K.: Bifurcation and route-to-chaos analyses for Mathieu-duffing oscillator by the incremental harmonic balance method. Nonlinear Dyn. 52(4), 403-414 (2008)
    • (2008) Nonlinear Dyn. , vol.52 , Issue.4 , pp. 403-414
    • Shen, J.1    Lin, K.2    Chen, S.3    Sze, K.4
  • 14
    • 0036502110 scopus 로고    scopus 로고
    • An alternate method to the alternating time-frequency method
    • 10.1023/A:1015238500024 1895219 1019.70001 10.1023/A:1015238500024
    • Rook, T.: An alternate method to the alternating time-frequency method. Nonlinear Dyn. 27, 327-339 (2002). doi: 10.1023/A:1015238500024
    • (2002) Nonlinear Dyn. , vol.27 , pp. 327-339
    • Rook, T.1
  • 15
    • 2542586138 scopus 로고    scopus 로고
    • Dynamic characteristics of a flexible bladed-rotor with coulomb damping due to tip-rub
    • 10.1016/S0022-460X(03)00647-3 10.1016/S0022-460X(03)00647-3
    • Sinha, S.K.: Dynamic characteristics of a flexible bladed-rotor with coulomb damping due to tip-rub. J. Sound Vib. 273(4-5), 875-919 (2004). doi: 10.1016/S0022-460X(03)00647-3
    • (2004) J. Sound Vib. , vol.273 , Issue.4-5 , pp. 875-919
    • Sinha, S.K.1
  • 16
    • 0037978988 scopus 로고    scopus 로고
    • Analytical formulation of friction interface elements for analysis of nonlinear multi-harmonic vibrations of bladed disks
    • 10.1115/1.1539868 10.1115/1.1539868
    • Petrov, E.P.; Ewins, D.J.: Analytical formulation of friction interface elements for analysis of nonlinear multi-harmonic vibrations of bladed disks. J. Turbomach. 125(2), 364-371 (2003). doi: 10.1115/1.1539868
    • (2003) J. Turbomach. , vol.125 , Issue.2 , pp. 364-371
    • Petrov, E.P.1    Ewins, D.J.2
  • 17
    • 0020269223 scopus 로고
    • A variable parameter incrementation method for dynamic instability of linear and nonlinear elastic systems
    • 10.1115/1.3162626 1097.34053 10.1115/1.3162626
    • Lau, S.L.; Cheung, Y.K.; Wu, S.Y.: A variable parameter incrementation method for dynamic instability of linear and nonlinear elastic systems. J. Appl. Mech. 49(4), 849-853 (1982). doi: 10.1115/1.3162626
    • (1982) J. Appl. Mech. , vol.49 , Issue.4 , pp. 849-853
    • Lau, S.L.1    Cheung, Y.K.2    Wu, S.Y.3
  • 18
    • 0024620165 scopus 로고
    • An alternating frequency/time domain method for calculating the steady-state response of nonlinear dynamic systems
    • 991104 0685.73036 10.1115/1.3176036
    • Cameron, T.M.; Griffin, J.H.: An alternating frequency/time domain method for calculating the steady-state response of nonlinear dynamic systems. J. Appl. Mech. 56(1), 149-154 (1989)
    • (1989) J. Appl. Mech. , vol.56 , Issue.1 , pp. 149-154
    • Cameron, T.M.1    Griffin, J.H.2
  • 19
    • 28844484998 scopus 로고
    • Impulsive parametric excitation: Theory
    • 0279.34030 10.1115/1.3422715
    • Hsu, C.S.: Impulsive parametric excitation: theory. J. Appl. Mech. 39(2), 551-558 (1972)
    • (1972) J. Appl. Mech. , vol.39 , Issue.2 , pp. 551-558
    • Hsu, C.S.1
  • 20
    • 0032139324 scopus 로고    scopus 로고
    • Fast Fourier nonlinear vibration analysis
    • 0928.74111 10.1007/s004660050347
    • Cardona, A.; Lerusse, A.; Géradin, M.: Fast Fourier nonlinear vibration analysis. Comput. Mech. 22(2), 128-142 (1998)
    • (1998) Comput. Mech. , vol.22 , Issue.2 , pp. 128-142
    • Cardona, A.1    Lerusse, A.2    Géradin, M.3
  • 21
    • 53849083425 scopus 로고    scopus 로고
    • Nonlinear normal modes, part ii: Toward a practical computation using numerical continuation techniques
    • 10.1016/j.ymssp.2008.04.003 10.1016/j.ymssp.2008.04.003
    • Peeters, M.; Viguié, R.; Sérandour, G.; Kerschen, G.; Golinval, J.C.: Nonlinear normal modes, part ii: toward a practical computation using numerical continuation techniques. Mech. Syst. Signal Process. 23(1), 195-216 (2009). doi: 10.1016/j.ymssp.2008.04.003
    • (2009) Mech. Syst. Signal Process. , vol.23 , Issue.1 , pp. 195-216
    • Peeters, M.1    Viguié, R.2    Sérandour, G.3    Kerschen, G.4    Golinval, J.C.5
  • 22
    • 70349807609 scopus 로고    scopus 로고
    • Modified shooting approach to the non-linear periodic forced response of isotropic/composite curved beams
    • 10.1016/j.ijnonlinmec.2009.08.004 10.1016/j.ijnonlinmec.2009.08.004
    • Ibrahim, S.; Patel, B.; Nath, Y.: Modified shooting approach to the non-linear periodic forced response of isotropic/composite curved beams. Int. J. Non-Linear Mech. 44(10), 1073-1084 (2009). doi: 10.1016/j.ijnonlinmec.2009.08. 004
    • (2009) Int. J. Non-Linear Mech. , vol.44 , Issue.10 , pp. 1073-1084
    • Ibrahim, S.1    Patel, B.2    Nath, Y.3
  • 23
    • 0042378498 scopus 로고    scopus 로고
    • An implicit transition matrix approach to stability analysis of flexible multi-body systems
    • 10.1023/A:1011488504973 1823730 0503.73031 10.1023/A:1011488504973
    • Bauchau, O.A.; Nikishkov, Y.G.: An implicit transition matrix approach to stability analysis of flexible multi-body systems. Multibody Syst. Dyn. 5, 279-301 (2001). doi: 10.1023/A:1011488504973
    • (2001) Multibody Syst. Dyn. , vol.5 , pp. 279-301
    • Bauchau, O.A.1    Nikishkov, Y.G.2
  • 24
    • 0035974953 scopus 로고    scopus 로고
    • A wavelet-Galerkin procedure to investigate time-periodic systems: Transient vibration and stability analysis
    • 10.1006/jsvi.2001.3610 10.1006/jsvi.2001.3610
    • Pernot, S.; Lamarque, C.H.: A wavelet-Galerkin procedure to investigate time-periodic systems: transient vibration and stability analysis. J. Sound Vib. 245(5), 845-875 (2001). doi: 10.1006/jsvi.2001.3610
    • (2001) J. Sound Vib. , vol.245 , Issue.5 , pp. 845-875
    • Pernot, S.1    Lamarque, C.H.2
  • 25
    • 0038106623 scopus 로고    scopus 로고
    • A wavelet-balance method to investigate the vibrations of nonlinear dynamical systems
    • 10.1023/A:1024263917587 1988887 1062.70503 10.1023/A:1024263917587
    • Pernot, S.; Lamarque, C.H.: A wavelet-balance method to investigate the vibrations of nonlinear dynamical systems. Nonlinear Dyn. 32, 33-70 (2003). doi: 10.1023/A:1024263917587
    • (2003) Nonlinear Dyn. , vol.32 , pp. 33-70
    • Pernot, S.1    Lamarque, C.H.2
  • 26
    • 77956647722 scopus 로고    scopus 로고
    • A harmonic-based method for computing the stability of periodic solutions of dynamical systems
    • 10.1016/j.crme.2010.07.020 1223.37106 10.1016/j.crme.2010.07.020
    • Lazarus, A.; Thomas, O.: A harmonic-based method for computing the stability of periodic solutions of dynamical systems. C. R.; Méc. 338(9), 510-517 (2010). doi: 10.1016/j.crme.2010.07.020
    • (2010) C. R.; Méc. , vol.338 , Issue.9 , pp. 510-517
    • Lazarus, A.1    Thomas, O.2
  • 30
    • 0028460381 scopus 로고
    • Harmonic balance analysis of general squeeze film damped multidegree-of-freedom rotor bearing systems
    • 10.1115/1.2928872 10.1115/1.2928872
    • Hahn, E.J.; Chen, P.Y.P.: Harmonic balance analysis of general squeeze film damped multidegree-of-freedom rotor bearing systems. J. Tribol. 116(3), 499-507 (1994). doi: 10.1115/1.2928872
    • (1994) J. Tribol. , vol.116 , Issue.3 , pp. 499-507
    • Hahn, E.J.1    Chen, P.Y.P.2
  • 32
    • 79952536943 scopus 로고    scopus 로고
    • Model reduction of nonlinear systems with external periodic excitations via construction of invariant manifolds
    • 10.1016/j.jsv.2010.12.013 10.1016/j.jsv.2010.12.013
    • Gabale, A.P.; Sinha, S.: Model reduction of nonlinear systems with external periodic excitations via construction of invariant manifolds. J. Sound Vib. 330(11), 2596-2607 (2011). doi: 10.1016/j.jsv.2010.12.013
    • (2011) J. Sound Vib. , vol.330 , Issue.11 , pp. 2596-2607
    • Gabale, A.P.1    Sinha, S.2
  • 33
    • 0002689020 scopus 로고
    • A method of computation for structural dynamics
    • Newmark, N.M.: A method of computation for structural dynamics. J. Eng. Mech. Div. 85(EM3), 2596-2607 (1959)
    • (1959) J. Eng. Mech. Div. , vol.85 , Issue.EM3 , pp. 2596-2607
    • Newmark, N.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.