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Volumn 42, Issue 10, 2007, Pages 1170-1185

Principal parametric resonances of a slender cantilever beam subject to axial narrow-band random excitation of its base

Author keywords

Almost sure stability; Bounded noise; Finite difference method; FPK equation; Narrow band random excitation; Principal parametric resonance; Slender cantilever beam; Stationary joint probability density; Steady state moment; Stochastic jump and bifurcation; The largest Lyapunov exponent

Indexed keywords

BESSEL FUNCTIONS; BIFURCATION (MATHEMATICS); EQUATIONS OF MOTION; FINITE DIFFERENCE METHOD; INTEGRODIFFERENTIAL EQUATIONS; LYAPUNOV METHODS; PERTURBATION TECHNIQUES; RESONANCE;

EID: 36049022798     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2007.09.002     Document Type: Article
Times cited : (38)

References (46)
  • 1
    • 85024532709 scopus 로고
    • Effects of longitudinal inertia upon the parametric response of elastic columns
    • Evensen H.A., and Even-Iwanowski R.M. Effects of longitudinal inertia upon the parametric response of elastic columns. ASME J. Appl. Mech. 33 2 (1966) 141-148
    • (1966) ASME J. Appl. Mech. , vol.33 , Issue.2 , pp. 141-148
    • Evensen, H.A.1    Even-Iwanowski, R.M.2
  • 3
    • 0018162077 scopus 로고
    • Non-linear flexural-flexural-torsional dynamics of inextensional beams-I: equations of motion
    • Crespo da silva M.R.M., and Glynn C.C. Non-linear flexural-flexural-torsional dynamics of inextensional beams-I: equations of motion. J. Struct. Mech. 6 4 (1978) 437-448
    • (1978) J. Struct. Mech. , vol.6 , Issue.4 , pp. 437-448
    • Crespo da silva, M.R.M.1    Glynn, C.C.2
  • 4
    • 0018152531 scopus 로고
    • Non-linear flexural-flexural-torsional dynamics of inextensional beams-II: forced motions
    • Crespo da silva M.R.M., and Glynn C.C. Non-linear flexural-flexural-torsional dynamics of inextensional beams-II: forced motions. J. Struct. Mech. 6 4 (1978) 449-461
    • (1978) J. Struct. Mech. , vol.6 , Issue.4 , pp. 449-461
    • Crespo da silva, M.R.M.1    Glynn, C.C.2
  • 5
    • 0024860195 scopus 로고
    • Non-linear non-planar parametric responses of an inextensional beam
    • Nayfeh A.H., and Pai P.F. Non-linear non-planar parametric responses of an inextensional beam. Int. J. Non-Linear Mech. 24 2 (1989) 138-158
    • (1989) Int. J. Non-Linear Mech. , vol.24 , Issue.2 , pp. 138-158
    • Nayfeh, A.H.1    Pai, P.F.2
  • 6
    • 0024865382 scopus 로고
    • The non-linear response of a slender beam carrying a lumped mass to a principal parametric excitation: theory and experiment
    • Zavodney L.D., and Nayfeh A.H. The non-linear response of a slender beam carrying a lumped mass to a principal parametric excitation: theory and experiment. Int. J. Non-Linear Mech. 24 2 (1989) 105-125
    • (1989) Int. J. Non-Linear Mech. , vol.24 , Issue.2 , pp. 105-125
    • Zavodney, L.D.1    Nayfeh, A.H.2
  • 7
    • 0001862560 scopus 로고    scopus 로고
    • Non-linear dynamics of a slender beam carrying a lumped mass with principal parametric and internal resonances
    • Kar R.C., and Dwivedy S.K. Non-linear dynamics of a slender beam carrying a lumped mass with principal parametric and internal resonances. Int. J. Non-Linear Mech. 34 3 (1999) 515-529
    • (1999) Int. J. Non-Linear Mech. , vol.34 , Issue.3 , pp. 515-529
    • Kar, R.C.1    Dwivedy, S.K.2
  • 8
    • 0029774649 scopus 로고    scopus 로고
    • Experimental verification of the importance of the nonlinear curvature in the response of a cantilever beam
    • Anderson T.J., Nayfeh A.H., and Balachandran B. Experimental verification of the importance of the nonlinear curvature in the response of a cantilever beam. ASME J. Vib. Acoust. 118 1 (1996) 21-27
    • (1996) ASME J. Vib. Acoust. , vol.118 , Issue.1 , pp. 21-27
    • Anderson, T.J.1    Nayfeh, A.H.2    Balachandran, B.3
  • 9
    • 0023306258 scopus 로고
    • Dynamics of a cantilever beam attached to a moving base
    • Kane T.R., Ryan R.R., and Banerjee A.K. Dynamics of a cantilever beam attached to a moving base. J. Guidance Control Dyn. 10 2 (1987) 139-151
    • (1987) J. Guidance Control Dyn. , vol.10 , Issue.2 , pp. 139-151
    • Kane, T.R.1    Ryan, R.R.2    Banerjee, A.K.3
  • 10
    • 0001565221 scopus 로고
    • Dynamics of flexible beams undergoing overall motions
    • Yoo H.H., Ryan R.R., and Scott R.A. Dynamics of flexible beams undergoing overall motions. J. Sound Vib. 181 2 (1995) 261-278
    • (1995) J. Sound Vib. , vol.181 , Issue.2 , pp. 261-278
    • Yoo, H.H.1    Ryan, R.R.2    Scott, R.A.3
  • 11
    • 0005460408 scopus 로고    scopus 로고
    • Dynamic modeling and stability analysis of axially oscillating cantilever beams
    • Hyun S.H., and Yoo H.H. Dynamic modeling and stability analysis of axially oscillating cantilever beams. J. Sound Vib. 228 3 (1999) 543-558
    • (1999) J. Sound Vib. , vol.228 , Issue.3 , pp. 543-558
    • Hyun, S.H.1    Yoo, H.H.2
  • 12
    • 0000075011 scopus 로고    scopus 로고
    • Dynamic stability of a slender beam with internal resonance under a large linear motion (in Chinese)
    • Feng Z.H., and Hu H.Y. Dynamic stability of a slender beam with internal resonance under a large linear motion (in Chinese). Acta Mech. Sin. 34 4 (2002) 389-400
    • (2002) Acta Mech. Sin. , vol.34 , Issue.4 , pp. 389-400
    • Feng, Z.H.1    Hu, H.Y.2
  • 13
    • 0037206999 scopus 로고    scopus 로고
    • Largest Lyapunov exponent and almost certain stability analysis of slender beams under a large linear motion of basement subject to narrow-band random parametric excitation
    • Feng Z.H., and Hu H.Y. Largest Lyapunov exponent and almost certain stability analysis of slender beams under a large linear motion of basement subject to narrow-band random parametric excitation. J. Sound Vib. 257 4 (2002) 733-752
    • (2002) J. Sound Vib. , vol.257 , Issue.4 , pp. 733-752
    • Feng, Z.H.1    Hu, H.Y.2
  • 14
    • 1342285427 scopus 로고    scopus 로고
    • Principal parametric and three-to-one internal resonances of flexible beams undergoing a large linear motion
    • Feng Z.H., and Hu H.Y. Principal parametric and three-to-one internal resonances of flexible beams undergoing a large linear motion. Acta Mech. Sin. 19 4 (2003) 355-364
    • (2003) Acta Mech. Sin. , vol.19 , Issue.4 , pp. 355-364
    • Feng, Z.H.1    Hu, H.Y.2
  • 15
    • 0036597064 scopus 로고    scopus 로고
    • Nonlinear dynamic modeling and periodic vibration of a cantilever beam subject to axial movement of basement
    • Feng Z.H., and Hu H.Y. Nonlinear dynamic modeling and periodic vibration of a cantilever beam subject to axial movement of basement. Acta Mech. Solida Sin. 15 2 (2002) 133-139
    • (2002) Acta Mech. Solida Sin. , vol.15 , Issue.2 , pp. 133-139
    • Feng, Z.H.1    Hu, H.Y.2
  • 16
    • 0031073272 scopus 로고    scopus 로고
    • Three-to-one internal resonances in hinged-clamped beams
    • Chin C.M., and Nayfeh A.H. Three-to-one internal resonances in hinged-clamped beams. Nonlinear Dyn. 12 2 (1997) 129-154
    • (1997) Nonlinear Dyn. , vol.12 , Issue.2 , pp. 129-154
    • Chin, C.M.1    Nayfeh, A.H.2
  • 17
    • 0032595407 scopus 로고    scopus 로고
    • Three-to-one internal resonances in parametrically excited hinged-clamped beams
    • Chin C.M., and Nayfeh A.H. Three-to-one internal resonances in parametrically excited hinged-clamped beams. Nonlinear Dyn. 20 2 (1999) 131-158
    • (1999) Nonlinear Dyn. , vol.20 , Issue.2 , pp. 131-158
    • Chin, C.M.1    Nayfeh, A.H.2
  • 18
    • 0001269931 scopus 로고    scopus 로고
    • Dynamics of a slender beam with an attached mass under combination parametric and internal resonances-part I: steady state response
    • Dwivedy S.K., and Kar R.C. Dynamics of a slender beam with an attached mass under combination parametric and internal resonances-part I: steady state response. J. Sound Vib. 221 5 (1999) 823-848
    • (1999) J. Sound Vib. , vol.221 , Issue.5 , pp. 823-848
    • Dwivedy, S.K.1    Kar, R.C.2
  • 19
    • 0035912242 scopus 로고    scopus 로고
    • Simultaneous combination, principal parametric and internal resonances in a slender beam with a lumped mass: three-mode interactions
    • Dwivedy S.K., and Kar R.C. Simultaneous combination, principal parametric and internal resonances in a slender beam with a lumped mass: three-mode interactions. J. Sound Vib. 242 1 (2001) 27-46
    • (2001) J. Sound Vib. , vol.242 , Issue.1 , pp. 27-46
    • Dwivedy, S.K.1    Kar, R.C.2
  • 20
    • 0035452980 scopus 로고    scopus 로고
    • Non-linear dynamics of a slender beam carrying a lumped mass under principal parametric resonance with three-mode interactions
    • Dwivedy S.K., and Kar R.C. Non-linear dynamics of a slender beam carrying a lumped mass under principal parametric resonance with three-mode interactions. Int. J. Non-Linear Mech. 36 6 (2001) 927-945
    • (2001) Int. J. Non-Linear Mech. , vol.36 , Issue.6 , pp. 927-945
    • Dwivedy, S.K.1    Kar, R.C.2
  • 21
    • 0035902169 scopus 로고    scopus 로고
    • Non-linear free vibrations of a rotating flexible arm
    • Hamdan M.N., and Al-Bedoor B.O. Non-linear free vibrations of a rotating flexible arm. J. Sound Vib. 242 5 (2001) 839-853
    • (2001) J. Sound Vib. , vol.242 , Issue.5 , pp. 839-853
    • Hamdan, M.N.1    Al-Bedoor, B.O.2
  • 22
    • 0024034644 scopus 로고
    • Multiple time scaling of the response of a Duffing oscillator to narrow-band random excitation
    • Rajan S., and Davies H.G. Multiple time scaling of the response of a Duffing oscillator to narrow-band random excitation. J. Sound Vib. 123 3 (1988) 497-506
    • (1988) J. Sound Vib. , vol.123 , Issue.3 , pp. 497-506
    • Rajan, S.1    Davies, H.G.2
  • 23
    • 0024088274 scopus 로고
    • Random superharmonic and subharmonic response: multiple time scaling of a Duffing oscillator
    • Davies H.G., and Rajan S. Random superharmonic and subharmonic response: multiple time scaling of a Duffing oscillator. J. Sound Vib. 126 2 (1988) 195-208
    • (1988) J. Sound Vib. , vol.126 , Issue.2 , pp. 195-208
    • Davies, H.G.1    Rajan, S.2
  • 24
    • 0025673024 scopus 로고
    • Response statistics of non-linear systems to combined deterministic and random excitations
    • Nayfeh A.H., and Serhan S.J. Response statistics of non-linear systems to combined deterministic and random excitations. Int. J. Non-Linear Mech. 25 5 (1990) 493-509
    • (1990) Int. J. Non-Linear Mech. , vol.25 , Issue.5 , pp. 493-509
    • Nayfeh, A.H.1    Serhan, S.J.2
  • 25
    • 0027912123 scopus 로고
    • Stochastic jump and bifurcation of a Duffing oscillator under narrow-band excitation
    • Zhu W.Q., Lu M.Q., and Wu Q.T. Stochastic jump and bifurcation of a Duffing oscillator under narrow-band excitation. J. Sound Vib. 165 2 (1993) 285-304
    • (1993) J. Sound Vib. , vol.165 , Issue.2 , pp. 285-304
    • Zhu, W.Q.1    Lu, M.Q.2    Wu, Q.T.3
  • 27
    • 0001201564 scopus 로고    scopus 로고
    • Principal response of Duffing oscillator to combined deterministic and narrow-band random parametric excitation
    • Rong H., Xu W., and Fang T. Principal response of Duffing oscillator to combined deterministic and narrow-band random parametric excitation. J. Sound Vib. 210 4 (1998) 483-515
    • (1998) J. Sound Vib. , vol.210 , Issue.4 , pp. 483-515
    • Rong, H.1    Xu, W.2    Fang, T.3
  • 28
    • 15944362620 scopus 로고    scopus 로고
    • Largest Lyapunov exponent for second-order linear systems under combined harmonic and random parametric excitations
    • Rong H.W., Meng G., Wang X.D., Xu W., and Fang T. Largest Lyapunov exponent for second-order linear systems under combined harmonic and random parametric excitations. J. Sound Vib. 283 5 (2005) 1250-1256
    • (2005) J. Sound Vib. , vol.283 , Issue.5 , pp. 1250-1256
    • Rong, H.W.1    Meng, G.2    Wang, X.D.3    Xu, W.4    Fang, T.5
  • 29
    • 0036722194 scopus 로고    scopus 로고
    • Response statistics of two-degree-of-freedom non-linear system to narrow-band random excitation
    • Rong H.W., Xu W., Wang X.D., Meng G., and Fang T. Response statistics of two-degree-of-freedom non-linear system to narrow-band random excitation. Int. J. Non-Linear Mech. 37 7 (2002) 1017-1028
    • (2002) Int. J. Non-Linear Mech. , vol.37 , Issue.7 , pp. 1017-1028
    • Rong, H.W.1    Xu, W.2    Wang, X.D.3    Meng, G.4    Fang, T.5
  • 30
    • 0036519582 scopus 로고    scopus 로고
    • Principal response of Van der Pol-Duffing Oscillator under combined deterministic and random parametric excitation (in Chinese)
    • Rong H.W., Xu W., Wang X.D., Meng G., and Fang T. Principal response of Van der Pol-Duffing Oscillator under combined deterministic and random parametric excitation (in Chinese). Appl. Math. Mech. 23 3 (2002) 273-282
    • (2002) Appl. Math. Mech. , vol.23 , Issue.3 , pp. 273-282
    • Rong, H.W.1    Xu, W.2    Wang, X.D.3    Meng, G.4    Fang, T.5
  • 31
    • 0025452258 scopus 로고
    • Invariant measures and Lyapunov exponents for generalized parameter fluctuations
    • Wedig W.V. Invariant measures and Lyapunov exponents for generalized parameter fluctuations. Struct. Saf. 8 1 (1990) 13-25
    • (1990) Struct. Saf. , vol.8 , Issue.1 , pp. 13-25
    • Wedig, W.V.1
  • 32
    • 0034324551 scopus 로고    scopus 로고
    • Stochastic averaging of strongly non-linear oscillators under combined harmonic and white noise excitations
    • Huang Z.L., Zhu W.Q., and Suzuki Y. Stochastic averaging of strongly non-linear oscillators under combined harmonic and white noise excitations. J. Sound Vib. 238 2 (2000) 233-256
    • (2000) J. Sound Vib. , vol.238 , Issue.2 , pp. 233-256
    • Huang, Z.L.1    Zhu, W.Q.2    Suzuki, Y.3
  • 33
    • 2442530701 scopus 로고    scopus 로고
    • Stochastic averaging of quasi-integrable Hamiltonian systems under combined harmonic and white noise excitations
    • Huang Z.L., and Zhu W.Q. Stochastic averaging of quasi-integrable Hamiltonian systems under combined harmonic and white noise excitations. Int. J. Non-Linear Mech. 39 9 (2004) 1421-1434
    • (2004) Int. J. Non-Linear Mech. , vol.39 , Issue.9 , pp. 1421-1434
    • Huang, Z.L.1    Zhu, W.Q.2
  • 34
    • 2342618243 scopus 로고    scopus 로고
    • Stochastic averaging of quasi-integrable Hamiltonian systems under bounded noise excitations
    • Huang Z.L., and Zhu W.Q. Stochastic averaging of quasi-integrable Hamiltonian systems under bounded noise excitations. Probabilistic Eng. Mech. 19 3 (2004) 219-228
    • (2004) Probabilistic Eng. Mech. , vol.19 , Issue.3 , pp. 219-228
    • Huang, Z.L.1    Zhu, W.Q.2
  • 35
    • 36049033882 scopus 로고    scopus 로고
    • R.L. Stratonovich, Topics in the Theory of Random Noise, vol. II, Gordon and Breach, New York, 1967.
  • 37
    • 36049009654 scopus 로고    scopus 로고
    • W. Wedig, Analysis and simulation of nonlinear stochastic systems, in: W. Schiehlen (Ed.), Nonlinear Dynamics in Engineering Systems, Springer, Berlin, 1989, pp. 337-344.
  • 39
    • 36048977800 scopus 로고    scopus 로고
    • S.T. Ariaratnam, Stochastic stability of viscoelastic systems under bounded noise excitation, in: A. Naess, S. Krenk (Eds.), IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics, Kluwer Academic Publishers, Dordrecht, 1996, pp. 11-18.
  • 40
    • 0038486195 scopus 로고    scopus 로고
    • Moment Lyapunov exponents of a two-dimensional system under bounded noise parametric excitation
    • Xie W.C. Moment Lyapunov exponents of a two-dimensional system under bounded noise parametric excitation. J. Sound Vib. 263 3 (2003) 593-616
    • (2003) J. Sound Vib. , vol.263 , Issue.3 , pp. 593-616
    • Xie, W.C.1
  • 41
    • 3042519294 scopus 로고    scopus 로고
    • Optimal feedback control of strongly non-linear systems excited by bounded noise
    • Zhu W.Q., Huang Z.L., Ko J.M., and Ni Y.Q. Optimal feedback control of strongly non-linear systems excited by bounded noise. J. Sound Vib. 274 3-5 (2004) 701-724
    • (2004) J. Sound Vib. , vol.274 , Issue.3-5 , pp. 701-724
    • Zhu, W.Q.1    Huang, Z.L.2    Ko, J.M.3    Ni, Y.Q.4
  • 42
    • 2342631981 scopus 로고    scopus 로고
    • Modeling of bounded stochastic processes
    • Cai G.Q., and Wu C. Modeling of bounded stochastic processes. Probabilistic Eng. Mech. 19 3 (2004) 197-203
    • (2004) Probabilistic Eng. Mech. , vol.19 , Issue.3 , pp. 197-203
    • Cai, G.Q.1    Wu, C.2
  • 43
    • 30344474624 scopus 로고    scopus 로고
    • Saturation and resonance of nonlinear system under bounded noise excitation
    • Rong H.W., Wang X.D., Xu W., and Fang T. Saturation and resonance of nonlinear system under bounded noise excitation. J. Sound Vib. 291 1-2 (2006) 48-59
    • (2006) J. Sound Vib. , vol.291 , Issue.1-2 , pp. 48-59
    • Rong, H.W.1    Wang, X.D.2    Xu, W.3    Fang, T.4
  • 44
    • 0000543733 scopus 로고
    • A multiplicative ergodic theorem, Lyapunov characteristic numbers for dynamical systems
    • Oseledec V.I. A multiplicative ergodic theorem, Lyapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc. 19 2 (1969) 197-231
    • (1969) Trans. Moscow Math. Soc. , vol.19 , Issue.2 , pp. 197-231
    • Oseledec, V.I.1
  • 45
    • 84955045119 scopus 로고
    • Simulation of multivariate and multidimensional random processes
    • Shinozuka M. Simulation of multivariate and multidimensional random processes. J. Acoust. Soc. Am. 49 1 (1971) 357-367
    • (1971) J. Acoust. Soc. Am. , vol.49 , Issue.1 , pp. 357-367
    • Shinozuka, M.1
  • 46
    • 0039400744 scopus 로고
    • Digital simulation of random processes and its applications
    • Shinozuka M., and Jan C.M. Digital simulation of random processes and its applications. J. Sound Vib. 25 1 (1972) 111-128
    • (1972) J. Sound Vib. , vol.25 , Issue.1 , pp. 111-128
    • Shinozuka, M.1    Jan, C.M.2


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