메뉴 건너뛰기




Volumn 40, Issue 5, 2003, Pages 955-963

Compact methodology for computing limit-cycle oscillations in aeroelasticity

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FINITE DIFFERENCE METHOD; FOURIER TRANSFORMS; NAVIER STOKES EQUATIONS; OSCILLATIONS; VELOCITY;

EID: 0242273112     PISSN: 00218669     EISSN: 15333868     Source Type: Journal    
DOI: 10.2514/2.6880     Document Type: Article
Times cited : (13)

References (61)
  • 1
    • 0034965813 scopus 로고    scopus 로고
    • Modeling of fluid-structure interaction
    • Dowell, E. H., and Hall, K. C., "Modeling of Fluid-Structure Interaction," Annual Reviews of Fluid Mechanics, Vol. 33, No. 1, 2001, pp. 445-490.
    • (2001) Annual Reviews of Fluid Mechanics , vol.33 , Issue.1 , pp. 445-490
    • Dowell, E.H.1    Hall, K.C.2
  • 3
    • 85003264299 scopus 로고
    • Ptrov-Galerkin finite elements in time for rigid-body dynamics
    • Borri, M., and Bottasso, C., "Ptrov-Galerkin Finite Elements in Time for Rigid-Body Dynamics," Journal of Guidance, Control, and Dynamics, Vol. 17, No. 5, 1994, pp. 1061-1068.
    • (1994) Journal of Guidance, Control, and Dynamics , vol.17 , Issue.5 , pp. 1061-1068
    • Borri, M.1    Bottasso, C.2
  • 4
    • 0028530579 scopus 로고
    • Air resonance of hingeless rotor helicopters in trimmed forward flight
    • Milgram, J. H., and Chopra, I., "Air Resonance of Hingeless Rotor Helicopters in Trimmed Forward Flight," Journal of the American Helicopter Society, Vol. 39, No. 4, 1994, pp. 46-59.
    • (1994) Journal of the American Helicopter Society , vol.39 , Issue.4 , pp. 46-59
    • Milgram, J.H.1    Chopra, I.2
  • 5
    • 84989498863 scopus 로고
    • Further developments towards a new virtual-pulse time integral methodology for general non-linear transient thermal analysis
    • Tamma, K. K., Chen, X., and Sha, D., "Further Developments Towards a New Virtual-Pulse Time Integral Methodology for General Non-Linear Transient Thermal Analysis," Communications in Numerical Methods in Engineering, Vol. 10, No. 12, 1994, pp. 961-971.
    • (1994) Communications in Numerical Methods in Engineering , vol.10 , Issue.12 , pp. 961-971
    • Tamma, K.K.1    Chen, X.2    Sha, D.3
  • 6
    • 0000450409 scopus 로고    scopus 로고
    • Towards a formal theory of development/evolution and characterization of time discretized operators for heat transfer
    • Tamma, K. K., Zhou, X., and Sha, D., "Towards a Formal Theory of Development/Evolution and Characterization of Time Discretized Operators for Heat Transfer," International Journal of Numerical Methods for Heat and Fluid Flow, Vol. 9, No. 3, 1999, pp. 348-380.
    • (1999) International Journal of Numerical Methods for Heat and Fluid Flow , vol.9 , Issue.3 , pp. 348-380
    • Tamma, K.K.1    Zhou, X.2    Sha, D.3
  • 7
    • 0035065913 scopus 로고    scopus 로고
    • A theory of development and design of generalized integration operators for computational structural dynamics
    • Tamma, K. K., Zhou, X., and Sha, D., "A Theory of Development and Design of Generalized Integration Operators for Computational Structural Dynamics," International Journal for Numerical Methods in Engineering, Vol. 50, No. 7, 2001, pp. 1619-1668.
    • (2001) International Journal for Numerical Methods in Engineering , vol.50 , Issue.7 , pp. 1619-1668
    • Tamma, K.K.1    Zhou, X.2    Sha, D.3
  • 8
    • 0031125212 scopus 로고    scopus 로고
    • Stick-slip motion of frictionally damped turbine airfoils: A Finite Element in Time (FET) approach
    • Wang, Y., "Stick-Slip Motion of Frictionally Damped Turbine Airfoils: A Finite Element in Time (FET) Approach," Journal of Vibration and Acoustics, Vol. 119, No. 4, 1997, pp. 236-242.
    • (1997) Journal of Vibration and Acoustics , vol.119 , Issue.4 , pp. 236-242
    • Wang, Y.1
  • 9
  • 10
    • 0033879119 scopus 로고    scopus 로고
    • Solving optimal control problems using hp-version finite elements in time
    • Warner, M. S., and Hodges, D. H., "Solving Optimal Control Problems Using hp-Version Finite Elements in Time," Journal of Guidance, Control, and Dynamics, Vol. 23, No. 1, 2000, pp. 86-95.
    • (2000) Journal of Guidance, Control, and Dynamics , vol.23 , Issue.1 , pp. 86-95
    • Warner, M.S.1    Hodges, D.H.2
  • 11
    • 85025237802 scopus 로고
    • Recent advances and applications of reduction methods
    • Noor, A. K., "Recent Advances and Applications of Reduction Methods," Applied Mechanics Review, Vol. 47, No. 5, 1994, pp. 125-145.
    • (1994) Applied Mechanics Review , vol.47 , Issue.5 , pp. 125-145
    • Noor, A.K.1
  • 12
    • 0000456941 scopus 로고    scopus 로고
    • Introduction to archetypal analysis of spatio-temporal dynamics
    • Stone, E., and Cutler, A., "Introduction to Archetypal Analysis of Spatio-Temporal Dynamics," Physica D, Vol. 96, No. 5, 1994, pp. 110-131.
    • (1996) Physica D , vol.96 , Issue.1 , pp. 110-131
    • Stone, E.1    Cutler, A.2
  • 13
    • 0000246863 scopus 로고
    • Turbulence and the dynamics of coherent structures, part I: Coherent structures
    • Sirovich, L., "Turbulence and the Dynamics of Coherent Structures, Part I: Coherent Structures," Quarterly of Applied Mathematics, Vol. XLV, No. 3, 1987, pp. 561-571.
    • (1987) Quarterly of Applied Mathematics , vol.45 , Issue.3 , pp. 561-571
    • Sirovich, L.1
  • 14
    • 0000234490 scopus 로고
    • Turbulence and the dynamics of coherent structures, Part II: Symmetries and transformations
    • Sirovich, L., "Turbulence and the Dynamics of Coherent Structures, Part II: Symmetries and Transformations," Quarterly of Applied Mathematics, Vol. XLV, No. 3, 1987, pp. 573-582.
    • (1987) Quarterly of Applied Mathematics , vol.45 , Issue.3 , pp. 573-582
    • Sirovich, L.1
  • 15
    • 0000246863 scopus 로고
    • Turbulence and the dynamics of coherent structures, Part III: Dynamics and scaling
    • Sirovich, L. "Turbulence and the Dynamics of Coherent Structures, Part III: Dynamics and Scaling," Quarterly of Applied Mathematics, Vol. XLV, No. 3, 1987, pp. 583-590.
    • (1987) Quarterly of Applied Mathematics , vol.45 , Issue.3 , pp. 583-590
    • Sirovich, L.1
  • 17
    • 0027952039 scopus 로고
    • Reynolds number similarity of orthogonal decomposition of the outer layer of turbulent wall flow
    • Liu, Z. C., Adrian, R. J., and Hanratty, P., "Reynolds Number Similarity of Orthogonal Decomposition of the Outer Layer of Turbulent Wall Flow," Physics of Fluids, Vol. 6, No. 8, 1994, pp. 2815-2819.
    • (1994) Physics of Fluids , vol.6 , Issue.8 , pp. 2815-2819
    • Liu, Z.C.1    Adrian, R.J.2    Hanratty, P.3
  • 18
    • 0028203123 scopus 로고
    • Normal modes of vibration for non-linear continuous systems
    • Shaw, S. W., and Pierre, C., "Normal Modes of Vibration for Non-Linear Continuous Systems," Journal of Sound and Vibration, Vol. 169, No. 3, 1994, pp. 319-347.
    • (1994) Journal of Sound and Vibration , vol.169 , Issue.3 , pp. 319-347
    • Shaw, S.W.1    Pierre, C.2
  • 19
    • 0021843385 scopus 로고
    • Multi-harmonic analysis of dry friction damped systems using an incremental harmonic balance method
    • Pierre, C., Ferri, A. A., and Dowell, E. H., "Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method," Journal of Applied Mechanics, Vol. 52, No. 2, 1985, pp. 985-964.
    • (1985) Journal of Applied Mechanics , vol.52 , Issue.2 , pp. 958-964
    • Pierre, C.1    Ferri, A.A.2    Dowell, E.H.3
  • 20
    • 0023168647 scopus 로고
    • Fast Galerkin method and its application to determine periodic solutions of non-linear oscillators
    • Ling, F. H., and Wu, X. X., "Fast Galerkin Method and Its Application to Determine Periodic Solutions of Non-Linear Oscillators," International Journal for Non-Linear Mechanics, Vol. 22, No. 2, 1987, pp. 89-98.
    • (1987) International Journal for Non-Linear Mechanics , vol.22 , Issue.2 , pp. 89-98
    • Ling, F.H.1    Wu, X.X.2
  • 23
    • 0003582543 scopus 로고
    • Cambridge Univ. Press, New York
    • Ott, E. Chaos in Dynamical Systems, Cambridge Univ. Press, New York, 1993, p. 25.
    • (1993) Chaos in Dynamical Systems , pp. 25
    • Ott, E.1
  • 26
    • 0000316251 scopus 로고    scopus 로고
    • System identification for Ott-Grebogi-Yorke controller design
    • Epureanu, B. I., and Dowell, E. H., "System Identification for Ott-Grebogi-Yorke Controller Design," Physical Review E, Vol. 56, No. 5, 1997, pp. 5327-5331.
    • (1997) Physical Review E , vol.56 , Issue.5 , pp. 5327-5331
    • Epureanu, B.I.1    Dowell, E.H.2
  • 27
    • 22244435280 scopus 로고    scopus 로고
    • On the optimality of the OGY control scheme
    • Epureanu, B. I., and Dowell, E. H., "On the Optimality of the OGY Control Scheme," Physica D, Vol. 116, No. 1-2, 1998, pp. 1-7.
    • (1998) Physica D , vol.116 , Issue.1-2 , pp. 1-7
    • Epureanu, B.I.1    Dowell, E.H.2
  • 28
    • 0032002879 scopus 로고    scopus 로고
    • Stabilization of unstable limit cycles in systems with limited controllability: Expanding the basin of convergence of OGY-type controllers
    • Epureanu, B. I., Trickey, S. T., and Dowell, E. H., "Stabilization of Unstable Limit Cycles in Systems with Limited Controllability: Expanding the Basin of Convergence of OGY-type Controllers," Nonlinear Dynamics, Vol. 15, No. 2, 1998, pp. 191-205.
    • (1998) Nonlinear Dynamics , vol.15 , Issue.2 , pp. 191-205
    • Epureanu, B.I.1    Trickey, S.T.2    Dowell, E.H.3
  • 29
    • 0030257466 scopus 로고    scopus 로고
    • Predicting chaos through an harmonic balance technique: An Application to the time-delayed Chua's circuit
    • Gilli, M., and Maggio, M., "Predicting Chaos Through an Harmonic Balance Technique: an Application to the Time-Delayed Chua's Circuit," IEEE Transactions on Circuits and Systems, Vol. 43, No. 1, 1996, pp. 872-874.
    • (1996) IEEE Transactions on Circuits and Systems , vol.43 , Issue.1 , pp. 872-874
    • Gilli, M.1    Maggio, M.2
  • 30
    • 0031197307 scopus 로고    scopus 로고
    • A frequency method for predicting limit cycle bifurcations
    • Basso, M., Genesio, R., and Tesi, A., "A Frequency Method for Predicting Limit Cycle Bifurcations," Nonlinear Dynamics, Vol. 13, No. 4, 1997, pp. 339-360.
    • (1997) Nonlinear Dynamics , vol.13 , Issue.4 , pp. 339-360
    • Basso, M.1    Genesio, R.2    Tesi, A.3
  • 32
    • 0026886828 scopus 로고
    • The limit cycles of the generalized Rayleigh-Lienard oscillator
    • Garcia-Margallo, J., and Bejarano, J. D., "The Limit Cycles of the Generalized Rayleigh-Lienard Oscillator," Journal of Sound and Vibration, Vol. 156, No. 2, 1992, pp. 283-301.
    • (1992) Journal of Sound and Vibration , vol.156 , Issue.2 , pp. 283-301
    • Garcia-Margallo, J.1    Bejarano, J.D.2
  • 33
    • 0028416854 scopus 로고
    • Bifurcations of limit cycles in periodically forced nonlinear systems: The harmonic balance approach
    • Piccardi, C., "Bifurcations of Limit Cycles in Periodically Forced Nonlinear Systems: the Harmonic Balance Approach," IEEE Transactions on Circuits and Systems, Vol. 41, No. 1, 1994, pp. 315-320.
    • (1994) IEEE Transactions on Circuits and Systems , vol.41 , Issue.1 , pp. 315-320
    • Piccardi, C.1
  • 34
    • 0030378971 scopus 로고    scopus 로고
    • Harmonic balance analysis of codimension-two bifurcations in periodic systems
    • Piccardi, C., "Harmonic Balance Analysis of Codimension-Two Bifurcations in Periodic Systems," IEEE Transactions on Circuits and Systems, Vol. 43, No. 1, 1996, pp. 1015-1018.
    • (1996) IEEE Transactions on Circuits and Systems , vol.43 , Issue.1 , pp. 1015-1018
    • Piccardi, C.1
  • 35
    • 0028460381 scopus 로고
    • Harmonic balance analysis of general squeeze film damped multi degree-of-freedom rotor bearing systems
    • Hahn, E. J., and Chen, P. Y. P., "Harmonic Balance Analysis of General Squeeze Film Damped Multi Degree-of-Freedom Rotor Bearing Systems," Journal of Tribology, Vol. 116, No. 1, 1994, pp. 499-507.
    • (1994) Journal of Tribology , vol.116 , Issue.1 , pp. 499-507
    • Hahn, E.J.1    Chen, P.Y.P.2
  • 36
    • 0025899854 scopus 로고
    • Effect of constant transverse force on chaotic oscillations of sinusoidally excited buckled beam
    • Higuchi, K., and Dowell, E. H., "Effect of Constant Transverse Force on Chaotic Oscillations of Sinusoidally Excited Buckled Beam," International Journal of Non-Linear Mechanics, Vol. 26, No. 3-4, 1991, pp. 419-426.
    • (1991) International Journal of Non-Linear Mechanics , vol.26 , Issue.3-4 , pp. 419-426
    • Higuchi, K.1    Dowell, E.H.2
  • 37
    • 0029375580 scopus 로고
    • Dynamic analysis of a brushless d.c. motor using a modified harmonic balance method
    • Lee, M. R., Padmanabhan, C., and Singh, R., "Dynamic Analysis of a Brushless d.c. Motor Using a Modified Harmonic Balance Method," Journal of Dynamic Systems, Measurement and Control, Vol. 117, No. 1, 1995, pp. 283-291.
    • (1995) Journal of Dynamic Systems, Measurement and Control , vol.117 , Issue.1 , pp. 283-291
    • Lee, M.R.1    Padmanabhan, C.2    Singh, R.3
  • 38
    • 0019607365 scopus 로고
    • Reexamination of stability of a two-dimensional finite panel exposed to an incompressible flow
    • Matsuzaki, Y., "Reexamination of Stability of a Two-Dimensional Finite Panel Exposed to an Incompressible Flow," Journal of Applied Mechanics, Vol. 48, No. 3, 1981, pp. 472-478.
    • (1981) Journal of Applied Mechanics , vol.48 , Issue.3 , pp. 472-478
    • Matsuzaki, Y.1
  • 39
    • 0026224286 scopus 로고
    • Effects of in-plane load on nonlinear panel flutter by incremental harmonic balance method
    • Yuen, S. W., and Lau, S. L., "Effects of In-Plane Load on Nonlinear Panel Flutter by Incremental Harmonic Balance Method," AIAA Journal, Vol. 29, No. 9, 1991, pp. 1472-1479.
    • (1991) AIAA Journal , vol.29 , Issue.9 , pp. 1472-1479
    • Yuen, S.W.1    Lau, S.L.2
  • 40
    • 0036572063 scopus 로고    scopus 로고
    • Computation of unsteady nonlinear flows in cascades using a harmonic balance technique
    • Hall, K. C., Thomas, J. P., and Clark, W. S., "Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique," AIAA Journal, Vol. 40, No. 5, 2002, pp. 879-886.
    • (2002) AIAA Journal , vol.40 , Issue.5 , pp. 879-886
    • Hall, K.C.1    Thomas, J.P.2    Clark, W.S.3
  • 41
    • 0022739184 scopus 로고
    • On the equivalence of the incremental harmonic balance method and the harmonic balance-newton raphson method
    • Ferri, A. A., "On the Equivalence of the Incremental Harmonic Balance Method and the Harmonic Balance-Newton Raphson Method," Journal of Applied Mechanics, Vol. 53, No. 1, 1986, pp. 455-457.
    • (1986) Journal of Applied Mechanics , vol.53 , Issue.1 , pp. 455-457
    • Ferri, A.A.1
  • 42
    • 0026839419 scopus 로고
    • Nonlinear vibrations of piecewise-linear systems by incremental harmonic balance method
    • Lau, S. L., and Zhang, W. S. "Nonlinear Vibrations of Piecewise-Linear Systems by Incremental Harmonic Balance Method," Journal of Applied Mechanics, Vol. 59, No. 1, 1992, pp. 153-160.
    • (1992) Journal of Applied Mechanics , vol.59 , Issue.1 , pp. 153-160
    • Lau, S.L.1    Zhang, W.S.2
  • 43
    • 0022131804 scopus 로고
    • A study of dynamic instability of plates by an extended incremental harmonic balance method
    • Pierre, C., and Dowell, E. H., "A Study of Dynamic Instability of Plates by an Extended Incremental Harmonic Balance Method," Journal of Applied Mechanics, Vol. 52, No. 5, 1985, pp. 693-697.
    • (1985) Journal of Applied Mechanics , vol.52 , Issue.5 , pp. 693-697
    • Pierre, C.1    Dowell, E.H.2
  • 45
    • 0012853542 scopus 로고
    • DERPER - An algorithm for the continuation of periodic solutions in ordinary differential equations
    • Holodniok, M., and Kubicek, M., "DERPER - An Algorithm for the Continuation of Periodic Solutions in Ordinary Differential Equations," Journal of Computational Physics, Vol. 55, No. 1, 1984, pp. 254-267.
    • (1984) Journal of Computational Physics , vol.55 , Issue.1 , pp. 254-267
    • Holodniok, M.1    Kubicek, M.2
  • 46
    • 0020936281 scopus 로고
    • Incremental harmonic balance method with multiple time scales for aperiodic vibration of nonlinear systems
    • Lau, S. L., Cheung, Y. K., and Wu, S. Y., "Incremental Harmonic Balance Method with Multiple Time Scales for Aperiodic Vibration of Nonlinear Systems," Journal of Applied Mechanics, Vol. 50, No. 4, 1983, pp. 871-876.
    • (1983) Journal of Applied Mechanics , vol.50 , Issue.4 , pp. 871-876
    • Lau, S.L.1    Cheung, Y.K.2    Wu, S.Y.3
  • 47
    • 0027593222 scopus 로고
    • Computation of limit cycles via higher order harmonic balance approximation
    • Moiola, J., and Chen, G., "Computation of Limit Cycles via Higher Order Harmonic Balance Approximation," IEEE Transactions on Automatic Control, Vol. 38, No. 1, 1993, pp. 782-790.
    • (1993) IEEE Transactions on Automatic Control , vol.38 , Issue.1 , pp. 782-790
    • Moiola, J.1    Chen, G.2
  • 48
    • 0031248942 scopus 로고    scopus 로고
    • Symbolic computation of harmonic balance equations
    • Jones, J. C. P., Zhuang, M., and Cankaya, I., "Symbolic Computation of Harmonic Balance Equations," International Journal of Control, Vol. 68, No. 3, 1997, pp. 449-460.
    • (1997) International Journal of Control , vol.68 , Issue.3 , pp. 449-460
    • Jones, J.C.P.1    Zhuang, M.2    Cankaya, I.3
  • 49
    • 0030086110 scopus 로고    scopus 로고
    • Efficient determination of higher-order periodic solutions using n-mode harmonic balance
    • Donescu, P., and Virgin, L. N., "Efficient Determination of Higher-Order Periodic Solutions Using n-Mode Harmonic Balance," Journal of Applied Mathematics, Vol. 56, No. 1, 1996, pp. 21-32.
    • (1996) Journal of Applied Mathematics , vol.56 , Issue.1 , pp. 21-32
    • Donescu, P.1    Virgin, L.N.2
  • 50
    • 0030147729 scopus 로고    scopus 로고
    • Periodic solutions of an unsymmetric oscillator including a comprehensive study of their stability characteristics
    • Donescu, P., Virgin, L. N., and Wu, J. J., "Periodic Solutions of an Unsymmetric Oscillator Including a Comprehensive Study of Their Stability Characteristics," Journal of Sound and Vibration, Vol. 192, No. 5, 1996, pp. 959-976.
    • (1996) Journal of Sound and Vibration , vol.192 , Issue.5 , pp. 959-976
    • Donescu, P.1    Virgin, L.N.2    Wu, J.J.3
  • 51
    • 0023965176 scopus 로고
    • Forced periodic vibration of unsymmetric piecewise-linear systems
    • Choi, Y. S., and Noah, S. T., "Forced Periodic Vibration of Unsymmetric Piecewise-Linear Systems," Journal of Sound and Vibration, Vol. 121, No, 1, 1988, pp. 117-126.
    • (1988) Journal of Sound and Vibration , vol.121 , Issue.1 , pp. 117-126
    • Choi, Y.S.1    Noah, S.T.2
  • 52
    • 0024620165 scopus 로고
    • An alternating frequency/time domain method for calculating the steady-state response of nonlinear dynamic systems
    • Cameron, T. M., and Griffin, J. H., "An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems," Journal of Applied Mechanics, Vol. 56, No. 3, 1989, pp. 149-154.
    • (1989) Journal of Applied Mechanics , vol.56 , Issue.3 , pp. 149-154
    • Cameron, T.M.1    Griffin, J.H.2
  • 53
    • 0028184352 scopus 로고
    • On non-linear dynamic analysis in the frequency domain: Algorithms and applications
    • Aprile, A., Benedetti, A., and Trombetti, T., "On Non-Linear Dynamic Analysis in the Frequency Domain: Algorithms and Applications," Earthquake Engineering and Structural Dynamics, Vol. 23, No. 1, 1994, pp. 363-388.
    • (1994) Earthquake Engineering and Structural Dynamics , vol.23 , Issue.1 , pp. 363-388
    • Aprile, A.1    Benedetti, A.2    Trombetti, T.3
  • 54
    • 0001759089 scopus 로고    scopus 로고
    • Reduced order models of unsteady transonic viscous flows in turbomachinery
    • Epureanu, B. I., Hall, K. C., and Dowell, E. H., "Reduced Order Models of Unsteady Transonic Viscous Flows in Turbomachinery," Journal Fluids and Structures, Vol. 18, No. 8, 2000, pp. 1215-1235.
    • (2000) Journal Fluids and Structures , vol.18 , Issue.8 , pp. 1215-1235
    • Epureanu, B.I.1    Hall, K.C.2    Dowell, E.H.3
  • 55
    • 0035527633 scopus 로고    scopus 로고
    • Reduced order models of unsteady viscous flows in turbomachinery using viscous-inviscid coupling
    • Epureanu, B. I., Hall, K. C., and Dowell, E. H., "Reduced Order Models of Unsteady Viscous Flows in Turbomachinery Using Viscous-Inviscid Coupling," Journal Fluids and Structures, Vol. 15, No. 2, 2001, pp. 255-276.
    • (2001) Journal Fluids and Structures , vol.15 , Issue.2 , pp. 255-276
    • Epureanu, B.I.1    Hall, K.C.2    Dowell, E.H.3
  • 56
    • 0024641167 scopus 로고
    • Periodic solutions in rotor dynamic systems with nonlinear supports: A general approach
    • Nataraj, C., and Nelson, H. D., "Periodic Solutions in Rotor Dynamic Systems with Nonlinear Supports: A General Approach," Journal of Sound and Vibration, Vol. 111, No. 4, 1989, pp. 187-193.
    • (1989) Journal of Sound and Vibration , vol.111 , Issue.4 , pp. 187-193
    • Nataraj, C.1    Nelson, H.D.2
  • 57
    • 0028426786 scopus 로고
    • A new receptance-based perturbative multi-harmonic balance method for the calculation of the steady state response of non-linear systems
    • Ren, Y., and Beards, C. F., "A New Receptance-Based Perturbative Multi-Harmonic Balance Method for the Calculation of the Steady State Response of Non-Linear Systems," Journal of Sound and Vibration, Vol. 172, No. 5, 1994, pp. 593-604.
    • (1994) Journal of Sound and Vibration , vol.172 , Issue.5 , pp. 593-604
    • Ren, Y.1    Beards, C.F.2
  • 59
    • 85003383696 scopus 로고
    • Weak hamiltonian finite element method for optimal control problems
    • Hodges, D. H., and Bless, R. R., "Weak Hamiltonian Finite Element Method for Optimal Control Problems," Journal of Guidance, Control, and Dynamics, Vol. 14, No. 1, 1991, pp. 148-156.
    • (1991) Journal of Guidance, Control, and Dynamics , vol.14 , Issue.1 , pp. 148-156
    • Hodges, D.H.1    Bless, R.R.2
  • 61
    • 84988913344 scopus 로고
    • Toeplitz Jacobian matrix for nonlinear periodic vibration
    • New York
    • Leung, A. Y. T., and Ge, T., "Toeplitz Jacobian Matrix for Nonlinear Periodic Vibration," Journal of Applied Mechanics, New York, Vol. 62, No. 1, 1995, pp. 709-717.
    • (1995) Journal of Applied Mechanics , vol.62 , Issue.1 , pp. 709-717
    • Leung, A.Y.T.1    Ge, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.