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Volumn 6 C, Issue , 2001, Pages 3039-3048

Amplitude nonlinear normal modes of piecewise linear systems

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); DEGREES OF FREEDOM (MECHANICS); EQUATIONS OF MOTION; FREQUENCY DOMAIN ANALYSIS; GALERKIN METHODS; INVARIANCE; MATHEMATICAL TRANSFORMATIONS; MODAL ANALYSIS; NUMERICAL METHODS; PIECEWISE LINEAR TECHNIQUES; TIME DOMAIN ANALYSIS; VECTORS; DESIGN; LINEAR SYSTEMS; VIBRATIONS (MECHANICAL);

EID: 0242584945     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper
Times cited : (1)

References (24)
  • 1
    • 0000091624 scopus 로고
    • Stability in the linear approximation of a periodic solution of a system of differential equations with discontinuous right-hand sides
    • Aizerman, M. A. and Gantmakher, F. R. Stability in the linear approximation of a periodic solution of a system of differential equations with discontinuous right-hand sides. Prikl. Mat. Mekh., 21(5):658-66, 1957.
    • (1957) Prikl. Mat. Mekh. , vol.21 , Issue.5 , pp. 658-669
    • Aizerman, M.A.1    Gantmakher, F.R.2
  • 3
    • 0025721176 scopus 로고
    • A method of examining steady state solutions of forced discrete systems with strong nonlinearities
    • Caughey, T. K. and Vakakis, A. F. A method of examining steady state solutions of forced discrete systems with strong nonlinearities. International Journal of Non-Linear Mechanics, 26:89-103, 1991.
    • (1991) International Journal of Non-Linear Mechanics , vol.26 , pp. 89-103
    • Caughey, T.K.1    Vakakis, A.F.2
  • 4
    • 0030173462 scopus 로고    scopus 로고
    • Normal modes for piecewise linear vibratory systems
    • Chen, S. L. and Shaw, S. W. Normal Modes for Piecewise Linear Vibratory Systems. Nonlinear Dynamics, 10(2):135-163, 1996.
    • (1996) Nonlinear Dynamics , vol.10 , Issue.2 , pp. 135-163
    • Chen, S.L.1    Shaw, S.W.2
  • 5
    • 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, 121:117-126, 1988.
    • (1988) Journal of Sound and Vibration , vol.121 , pp. 117-126
    • Choi, Y.S.1    Noah, S.T.2
  • 6
    • 38249017872 scopus 로고
    • Frequency response characteristics of a multi-degree-of-freedom system with clearances
    • Comparin, R. J. and Singh, R. Frequency response characteristics of a multi-degree-of-freedom system with clearances. Journal of Sound and Vibration, 142:101-124, 1990.
    • (1990) Journal of Sound and Vibration , vol.142 , pp. 101-124
    • Comparin, R.J.1    Singh, R.2
  • 7
    • 0001407377 scopus 로고
    • The existence of periodic solutions and normal mode vibrations in nonlinear systems
    • Cooke, C. and Struble, R. The existence of periodic solutions and normal mode vibrations in nonlinear systems. Quarterly of Applied Mathematics, 24:177-193, 1966.
    • (1966) Quarterly of Applied Mathematics , vol.24 , pp. 177-193
    • Cooke, C.1    Struble, R.2
  • 9
    • 0003285244 scopus 로고
    • Nonlinear oscillations, dynamical systems and bifurcations of vector fields
    • New York: Springer-Verlag
    • Guckenheimer, J. and Holmes, P. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Applied Mathematical Sciences 42. New York: Springer-Verlag, 1989.
    • (1989) Applied Mathematical Sciences , vol.42
    • Guckenheimer, J.1    Holmes, P.2
  • 10
    • 0032216922 scopus 로고    scopus 로고
    • The stability of periodic solutions of discontinuity systems that intersect several surfaces of discontinuity
    • Ivanov, A. P. The Stability of Periodic Solutions of Discontinuity Systems that Intersect Several Surfaces of Discontinuity. J. Appl. Maths Mechs, 62(5):677-685, 1998.
    • (1998) J. Appl. Maths Mechs , vol.62 , Issue.5 , pp. 677-685
    • Ivanov, A.P.1
  • 11
    • 38249017901 scopus 로고
    • Chaotic behavior of some piecewise linear systems, part I: Systems with set-up spring or with unsymmetric elasticity
    • Mahfouz, I. A. and Badrakhan, F. Chaotic behavior of some piecewise linear systems, part I: systems with set-up spring or with unsymmetric elasticity. Journal of Sound and Vibration, 143:255-288, 1990.
    • (1990) Journal of Sound and Vibration , vol.143 , pp. 255-288
    • Mahfouz, I.A.1    Badrakhan, F.2
  • 12
    • 0019065472 scopus 로고
    • An application of poincaré map to the stability of nonlinear normal modes
    • Month, L. A. and Rand, R. H. An application of Poincaré map to the stability of nonlinear normal modes. Journal of Applied Mechanics, 47:645-651, 1980.
    • (1980) Journal of Applied Mechanics , vol.47 , pp. 645-651
    • Month, L.A.1    Rand, R.H.2
  • 13
    • 0001407377 scopus 로고
    • On the existence of normal mode vibrations in nonlinear systems
    • Pak, C. and Rosenberg, R. On the existence of normal mode vibrations in nonlinear systems. Quarterly of Applied Mathematics, 26:403-416, 1968.
    • (1968) Quarterly of Applied Mathematics , vol.26 , pp. 403-416
    • Pak, C.1    Rosenberg, R.2
  • 14
    • 4243423914 scopus 로고    scopus 로고
    • Reduced order modeling of nonlinear structural systems using nonlinear normal modes and invariant manifolds
    • PhD thesis, The University of Michigan
    • Pesheck, Eric. Reduced Order Modeling of Nonlinear Structural Systems using Nonlinear Normal Modes and Invariant Manifolds. PhD thesis, The University of Michigan, 2000.
    • (2000)
    • Pesheck, E.1
  • 15
    • 0001394731 scopus 로고
    • Bifurcaion of nonlinear normal modes in a class of 2 degrees of freedom systems
    • Rand, R., Pak, C. and Vakakis, A. Bifurcaion of nonlinear normal modes in a class of 2 degrees of freedom systems. Acta Mechanica, 3:129-145, 1992.
    • (1992) Acta Mechanica , vol.3 , pp. 129-145
    • Rand, R.1    Pak, C.2    Vakakis, A.3
  • 17
    • 33645049419 scopus 로고
    • On nonlinear vibrations of systems with many degrees of freedom
    • Rosenberg, R. M. On nonlinear vibrations of systems with many degrees of freedom. Advances in Applied Mechanics, 9:155-242, 1966.
    • (1966) Advances in Applied Mechanics , vol.9 , pp. 155-242
    • Rosenberg, R.M.1
  • 18
    • 0003860399 scopus 로고    scopus 로고
    • From equilibrium to chaos - Practical bifurcation and stability analysis
    • Elsevier Science Publishing Co., Inc.
    • Seydel, R. From equilibrium to chaos - practical bifurcation and stability analysis. Elsevier Science Publishing Co., Inc., 1998.
    • (1998)
    • Seydel, R.1
  • 19
    • 0021097823 scopus 로고
    • A periodically forced piece-wise linear oscillator
    • Shaw, S. W. and Holmes, P. J. A periodically forced piece-wise linear oscillator. Journal of Sound and Vibration, 90:129-155, 1983.
    • (1983) Journal of Sound and Vibration , vol.90 , pp. 129-155
    • Shaw, S.W.1    Holmes, P.J.2
  • 20
    • 0026420003 scopus 로고
    • Non-linear normal modes and invariant manifolds
    • Shaw, S. W. and Pierre, C. Non-linear normal modes and invariant manifolds. Journal of Sound and Vibration, 150(1):170-173, 1991.
    • (1991) Journal of Sound and Vibration , vol.150 , Issue.1 , pp. 170-173
    • Shaw, S.W.1    Pierre, C.2
  • 21
    • 0027911991 scopus 로고
    • Normal modes for nonlinear vibratory systems
    • Shaw, S. W. and Pierrer, C. Normal modes for nonlinear vibratory systems. Journal of Sound and Vibration, 164:85-124, 1993.
    • (1993) Journal of Sound and Vibration , vol.164 , pp. 85-124
    • Shaw, S.W.1    Pierrer, C.2
  • 22
    • 0028203123 scopus 로고
    • Normal modes of vibration for nonlinear continuous systems
    • Shaw, S. W. and Pierrer, C. Normal modes of vibration for nonlinear continuous systems. Journal of Sound and Vibration, 169:319-347, 1994.
    • (1994) Journal of Sound and Vibration , vol.169 , pp. 319-347
    • Shaw, S.W.1    Pierrer, C.2
  • 24
    • 0028463625 scopus 로고
    • Non-linear real and complex modes of conewise linear systems
    • Zuo, L. and Curnier, A. Non-linear Real and Complex Modes of Conewise Linear Systems. Journal of Sound and Vibration, 174(3):289-313, 1994.
    • (1994) Journal of Sound and Vibration , vol.174 , Issue.3 , pp. 289-313
    • Zuo, L.1    Curnier, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.