메뉴 건너뛰기




Volumn 330, Issue 22, 2011, Pages 5382-5400

A general solution procedure for vibrations of systems with cubic nonlinearities and nonlinear/time-dependent internal boundary conditions

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL EXPRESSIONS; APPROXIMATE ANALYTICAL METHODS; CLOSED FORM SOLUTIONS; CONTINUOUS SYSTEM; COUPLED BOUNDARY CONDITIONS; CUBIC NONLINEARITIES; GENERAL SOLUTIONS; INTERMEDIATE ELEMENT; INTERNAL BOUNDARY CONDITIONS; MULTIPLE TIMESCALES; NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS; PRIMARY RESONANCE; SOLUTION PROCEDURE; SUBDOMAIN; TIME-DEPENDENT; VIBRATION CHARACTERISTICS;

EID: 79961000310     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2011.06.001     Document Type: Article
Times cited : (91)

References (49)
  • 3
    • 0021505251 scopus 로고
    • A note on the vibrations of restrained beams and rods with point masses
    • DOI 10.1016/0022-460X(84)90633-3
    • M. Gurgoze A note on the vibrations of restrained beams and rods with point masses Journal of Sound and Vibration 96 4 1984 461 468 (Pubitemid 15454916)
    • (1984) Journal of Sound and Vibration , vol.96 , Issue.4 , pp. 461-468
    • Gurgoze, M.1
  • 4
    • 0026241281 scopus 로고
    • Free and forced vibrations of a restrained uniform beam carrying an intermediate lumped mass and a rotary inertia
    • M.N. Hamdan, and B.A. Jubran Free and forced vibrations of a restrained uniform beam carrying an intermediate lumped mass and a rotary inertia Journal of Sound and Vibration 150 2 1991 203 216
    • (1991) Journal of Sound and Vibration , vol.150 , Issue.2 , pp. 203-216
    • Hamdan, M.N.1    Jubran, B.A.2
  • 5
    • 0025254751 scopus 로고
    • Free vibration analysis of a uniform cantilever beam with point masses by an analytical-and-numerical-combined method
    • J.S. Wu, and T.L. Lin Free vibration analysis of a uniform cantilever beam with point masses by an analytical-and-numerical-combined method Journal of Sound and Vibration 136 2 1990 201 213
    • (1990) Journal of Sound and Vibration , vol.136 , Issue.2 , pp. 201-213
    • Wu, J.S.1    Lin, T.L.2
  • 6
    • 0033749008 scopus 로고    scopus 로고
    • Dynamic analysis of a uniform analysis of a uniform cantilever beam carrying a number of elastically mounted point masses with damper
    • J.S. Wu, and D.W. Chen Dynamic analysis of a uniform analysis of a uniform cantilever beam carrying a number of elastically mounted point masses with damper Journal of Sound and Vibration 229 3 2000 549 578
    • (2000) Journal of Sound and Vibration , vol.229 , Issue.3 , pp. 549-578
    • Wu, J.S.1    Chen, D.W.2
  • 7
    • 0242405931 scopus 로고    scopus 로고
    • Natural frequencies of a beammass system in transverse vibration: Rayleigh estimation versus eigen analysis solutions
    • K.H. Low Natural frequencies of a beammass system in transverse vibration: Rayleigh estimation versus eigen analysis solutions International Journal of Mechanical Sciences 45 67 2003 981 993
    • (2003) International Journal of Mechanical Sciences , vol.45 , Issue.67 , pp. 981-993
    • Low, K.H.1
  • 8
    • 34247180716 scopus 로고    scopus 로고
    • Transverse vibration of Bernoulli-Euler beams carrying point masses and taking into account their rotatory inertia: Exact solution
    • DOI 10.1016/j.jsv.2006.12.028, PII S0022460X07000855
    • S. Miaz, D.V. Bambill, C.A. Rossit, and P.A.A. Laura Transverse vibration of BernoulliEuler beams carrying point masses and taking into account their rotatory inertia: exact solution Journal of Sound and Vibration 303 35 2007 895 908 (Pubitemid 46617615)
    • (2007) Journal of Sound and Vibration , vol.303 , Issue.3-5 , pp. 895-908
    • Maiz, S.1    Bambill, D.V.2    Rossit, C.A.3    Laura, P.A.A.4
  • 9
    • 38749102303 scopus 로고    scopus 로고
    • A continuous-mass TMM for free vibration analysis of a non-uniform beam with various boundary conditions and carrying multiple concentrated elements
    • J.S. Wu, and C.T. Chen A continuous-mass TMM for free vibration analysis of a non-uniform beam with various boundary conditions and carrying multiple concentrated elements Journal of Sound and Vibration 311 35 2008 1420 1430
    • (2008) Journal of Sound and Vibration , vol.311 , Issue.35 , pp. 1420-1430
    • Wu, J.S.1    Chen, C.T.2
  • 10
    • 34548623104 scopus 로고    scopus 로고
    • Vibration of beams with arbitrary discontinuities and boundary conditions
    • DOI 10.1016/j.jsv.2007.06.071, PII S0022460X07004981
    • J. Wang, and P. Qiao Vibration of beams with arbitrary discontinuities and boundary conditions Journal of Sound and Vibration 308 12 2007 12 27 (Pubitemid 47404565)
    • (2007) Journal of Sound and Vibration , vol.308 , Issue.1-2 , pp. 12-27
    • Wang, J.1    Qiao, P.2
  • 11
    • 0028387071 scopus 로고
    • A comparison of two perturbation methods for vibrations of systems with quadratic and cubic nonlinearities
    • M. Pakdemirli A comparison of two perturbation methods for vibrations of systems with quadratic and cubic nonlinearities Mechanics Research Communications 21 2 1994 203 208
    • (1994) Mechanics Research Communications , vol.21 , Issue.2 , pp. 203-208
    • Pakdemirli, M.1
  • 12
    • 0000281185 scopus 로고
    • Comparison of direct-perturbation methods with discretization- perturbation methods for nonlinear vibrations
    • M. Pakdemirli, and H. Boyaci Comparison of direct-perturbation methods with discretization-perturbation methods for nonlinear vibrations Journal of Sound and Vibration 186 1995 837 845
    • (1995) Journal of Sound and Vibration , vol.186 , pp. 837-845
    • Pakdemirli, M.1    Boyaci, H.2
  • 13
    • 0031555691 scopus 로고    scopus 로고
    • The direct-perturbation method versus the discretization-perturbation method: Linear systems
    • M. Pakdemirli, and H. Boyaci The direct perturbation method versus the discretization perturbation method: linear systems Journal of Sound and Vibration 199 5 1997 825 832 (Pubitemid 127402965)
    • (1997) Journal of Sound and Vibration , vol.199 , Issue.5 , pp. 825-832
    • Pakdemirli, M.1    Boyaci, H.2
  • 14
    • 0001678783 scopus 로고    scopus 로고
    • A comparison of different versions of the method of multiple scales for partial differential equations
    • H. Boyaci, and M. Pakdemirli A comparison of different versions of the method of multiple scales for partial differential equations Journal of Sound and Vibration 204 4 1997 595 607 (Pubitemid 127401729)
    • (1997) Journal of Sound and Vibration , vol.204 , Issue.4 , pp. 595-607
    • Boyaci, H.1    Pakdemirli, M.2
  • 15
    • 0035807258 scopus 로고    scopus 로고
    • Vibrations of continuous systems with a general operator notation suitable for perturbative calculations
    • DOI 10.1006/jsvi.2001.3691
    • M. Pakdemirli Vibrations of continuous systems with a general operator notation suitable for perturbative calculations Journal of Sound and Vibration 246 5 2001 841 851 (Pubitemid 33013605)
    • (2001) Journal of Sound and Vibration , vol.246 , Issue.5 , pp. 841-851
    • Pakdemirli, M.1
  • 16
    • 0035521099 scopus 로고    scopus 로고
    • A general solution procedure for coupled systems with arbitrary internal resonances
    • DOI 10.1016/S0093-6413(02)00213-6, PII S0093641302002136
    • M. Pakdemirli A general solution procedure for coupled systems with arbitrary internal resonances Mechanics Research Communications 28 6 2001 617 622 (Pubitemid 34191949)
    • (2001) Mechanics Research Communications , vol.28 , Issue.6 , pp. 617-622
    • Pakdemirli, M.1
  • 17
    • 0345714960 scopus 로고    scopus 로고
    • Three-to-one internal resonances in a general cubic non-linear continuous system
    • M. Pakdemirli, and E. Ozkaya Three-to-one internal resonances in a general cubic non-linear continuous system Journal of Sound and Vibration 268 2003 543 553
    • (2003) Journal of Sound and Vibration , vol.268 , pp. 543-553
    • Pakdemirli, M.1    Ozkaya, E.2
  • 18
    • 11044233391 scopus 로고    scopus 로고
    • Two-to-one internal resonances in continuous systems with arbitrary quadratic nonlinearities
    • M. Pakdemirli, and E. Ozkaya Two-to-one internal resonances in continuous systems with arbitrary quadratic nonlinearities Arabian Journal for Science and Engineering 29 1C 2004 99 112 (Mechanical Vibration and Noise Theme Issue) (Pubitemid 40044656)
    • (2004) Arabian Journal for Science and Engineering , vol.29 , Issue.1 C , pp. 99-112
    • Pakdemirli, M.1    Ozkaya, E.2
  • 19
    • 0001742916 scopus 로고    scopus 로고
    • Direct treatment and discretizations of non-linear spatially continuous systems
    • W. Lacarbonara Direct treatment and discretizations of non-linear spatially continuous systems Journal of Sound and Vibration 221 1999 849 866 (Pubitemid 129602588)
    • (1999) Journal of Sound and Vibration , vol.221 , Issue.5 , pp. 849-866
    • Lacarbonara, W.1
  • 20
    • 0032097205 scopus 로고    scopus 로고
    • Reduced order models of weakly nonlinear spatially continuous systems
    • A.H. Nayfeh Reduced order models of weakly nonlinear spatially continuous systems Nonlinear Dynamics 16 1998 105 125
    • (1998) Nonlinear Dynamics , vol.16 , pp. 105-125
    • Nayfeh, A.H.1
  • 21
    • 67649807493 scopus 로고    scopus 로고
    • A general solution procedure for the forced vibrations of a continuous system with cubic nonlinearities: Primary resonance case
    • B.B. Ozhan, and M. Pakdemirli A general solution procedure for the forced vibrations of a continuous system with cubic nonlinearities: primary resonance case Journal of Sound and Vibration 325 45 2009 894 906
    • (2009) Journal of Sound and Vibration , vol.325 , Issue.45 , pp. 894-906
    • Ozhan, B.B.1    Pakdemirli, M.2
  • 22
    • 77249166493 scopus 로고    scopus 로고
    • A general solution procedure for the forced vibrations of a continuous system with cubic nonlinearities: Three-to-one internal resonances with external excitation
    • B.B. Ozhan, and M. Pakdemirli A general solution procedure for the forced vibrations of a continuous system with cubic nonlinearities: three-to-one internal resonances with external excitation Journal of Sound and Vibration 329 13 2010 2603 2615
    • (2010) Journal of Sound and Vibration , vol.329 , Issue.13 , pp. 2603-2615
    • Ozhan, B.B.1    Pakdemirli, M.2
  • 23
    • 77953326525 scopus 로고    scopus 로고
    • Asymptotic analysis on nonlinear vibration of axially accelerating viscoelastic strings with the standard linear solid model
    • L.Q. Chen, and H. Chen Asymptotic analysis on nonlinear vibration of axially accelerating viscoelastic strings with the standard linear solid model Journal of Engineering Mathematics 67 2010 205 218
    • (2010) Journal of Engineering Mathematics , vol.67 , pp. 205-218
    • Chen, L.Q.1    Chen, H.2
  • 24
    • 43049103745 scopus 로고    scopus 로고
    • Nonlinear transversal vibration and stability of an axially moving viscoelastic string supported by a partial viscoelastic guide
    • M.H. Ghayesh Nonlinear transversal vibration and stability of an axially moving viscoelastic string supported by a partial viscoelastic guide Journal of Sound and Vibration 314 2008 757 774
    • (2008) Journal of Sound and Vibration , vol.314 , pp. 757-774
    • Ghayesh, M.H.1
  • 25
    • 54149118730 scopus 로고    scopus 로고
    • Non-linear parametric vibration and stability of axially moving visco-elastic Rayleigh beams
    • M.H. Ghayesh, and S. Balar Non-linear parametric vibration and stability of axially moving visco-elastic Rayleigh beams International Journal of Solids and Structures 45 2008 6451 6467
    • (2008) International Journal of Solids and Structures , vol.45 , pp. 6451-6467
    • Ghayesh, M.H.1    Balar, S.2
  • 26
    • 67650086635 scopus 로고    scopus 로고
    • Stability characteristics of an axially accelerating string supported by an elastic foundation
    • M.H. Ghayesh Stability characteristics of an axially accelerating string supported by an elastic foundation Mechanism and Machine Theory 44 2009 1964 1979
    • (2009) Mechanism and Machine Theory , vol.44 , pp. 1964-1979
    • Ghayesh, M.H.1
  • 27
    • 77952884256 scopus 로고    scopus 로고
    • Non-linear parametric vibration and stability analysis for two dynamic models of axially moving Timoshenko beams
    • M.H. Ghayesh, and S. Balar Non-linear parametric vibration and stability analysis for two dynamic models of axially moving Timoshenko beams Applied Mathematical Modeling 34 2010 2850 2859
    • (2010) Applied Mathematical Modeling , vol.34 , pp. 2850-2859
    • Ghayesh, M.H.1    Balar, S.2
  • 28
    • 77249095069 scopus 로고    scopus 로고
    • Parametric vibrations and stability of an axially accelerating string guided by a non-linear elastic foundation
    • M.H. Ghayesh Parametric vibrations and stability of an axially accelerating string guided by a non-linear elastic foundation International Journal of Non-Linear Mechanics 45 2010 382 394
    • (2010) International Journal of Non-Linear Mechanics , vol.45 , pp. 382-394
    • Ghayesh, M.H.1
  • 29
    • 79958844251 scopus 로고    scopus 로고
    • Nonlinear dynamic response of axially moving, stretched viscoelastic strings
    • M.H. Ghayesh, and N. Moradian Nonlinear dynamic response of axially moving, stretched viscoelastic strings Archive of Applied Mechanics 81 2011 781 799
    • (2011) Archive of Applied Mechanics , vol.81 , pp. 781-799
    • Ghayesh, M.H.1    Moradian, N.2
  • 34
    • 0018992330 scopus 로고
    • Component mode analysis of nonlinear and nonconservative systems
    • E.H. Dowell Component mode analysis of nonlinear and nonconservative systems ASME Journal of Applied Mechanics 47 1980 172 176 (Pubitemid 11447846)
    • (1980) Journal of Applied Mechanics, Transactions ASME , vol.47 , Issue.1 , pp. 172-176
    • Dowell, E.H.1
  • 35
    • 0022736445 scopus 로고
    • On the effects of nonlinear elastic foundation on free vibration of beams
    • V. Birman On the effects of nonlinear elastic foundation on free vibration of beams ASME Journal of Applied Mechanics 53 1986 471 473 (Pubitemid 16571342)
    • (1986) Journal of Applied Mechanics, Transactions ASME , vol.53 , Issue.2 , pp. 471-473
    • Birman, V.1
  • 37
    • 0030647736 scopus 로고    scopus 로고
    • Non-liner vibrations of a beam-mass system under different boundary conditions
    • E. Ozkaya, M. Pakdemirli, and H.R. Oz Non-linear vibrations of a beam-mass system under different boundary conditions Journal of Sound and Vibration 199 1997 679 696 (Pubitemid 127402769)
    • (1997) Journal of Sound and Vibration , vol.199 , Issue.4 , pp. 679-696
    • Ozkaya, E.1    Pakdemirli, M.2    Oz, H.R.3
  • 38
    • 0345328127 scopus 로고    scopus 로고
    • Non-linear vibrations of a simple-simple beam with a non-ideal support in between
    • M. Pakdemirli, and H. Boyac Non-linear vibrations of a simple-simple beam with a non-ideal support in between Journal of Sound and Vibration 268 2003 331 341
    • (2003) Journal of Sound and Vibration , vol.268 , pp. 331-341
    • Pakdemirli, M.1    Boyac, H.2
  • 39
    • 77950863354 scopus 로고    scopus 로고
    • Three-dimensional dynamics of a cantilevered pipe conveying fluid, additionally supported by an intermediate spring array
    • M.H. Ghayesh, and M.P. Païdoussis Three-dimensional dynamics of a cantilevered pipe conveying fluid, additionally supported by an intermediate spring array International Journal of Non-Linear Mechanics 45 2010 507 524
    • (2010) International Journal of Non-Linear Mechanics , vol.45 , pp. 507-524
    • Ghayesh, M.H.1    Païdoussis, M.P.2
  • 40
    • 79953678933 scopus 로고    scopus 로고
    • Three-dimensional dynamics of a fluid-conveying cantilevered pipe fitted with an additional spring-support and an end-mass
    • M.H. Ghayesh, M.P. Païdoussis, and Y. Modarres-Sadeghi Three-dimensional dynamics of a fluid-conveying cantilevered pipe fitted with an additional spring-support and an end-mass Journal of Sound and Vibration 330 2011 2869 2899
    • (2011) Journal of Sound and Vibration , vol.330 , pp. 2869-2899
    • Ghayesh, M.H.1    Païdoussis, M.P.2    Modarres-Sadeghi, Y.3
  • 41
    • 79960972613 scopus 로고    scopus 로고
    • Dynamics of a fluid-conveying cantilevered pipe with intermediate spring support
    • M.H. Ghayesh, M.P. Païdoussis, Dynamics of a fluid-conveying cantilevered pipe with intermediate spring support, ASME Conference Proceedings, 2010, pp. 893902.
    • (2010) ASME Conference Proceedings , pp. 893902
    • Ghayesh, M.H.1
  • 42
    • 0036778875 scopus 로고    scopus 로고
    • Kelvin-Voigt versus Bürgers internal damping in modeling of axially moving viscoelastic web
    • DOI 10.1016/S0020-7462(01)00142-1, PII S0020746201001421
    • K. Marynowski, and T. Kapitaniak KelvinVoigt versus burgers internal damping in modeling of axially moving viscoelastic web International Journal of Non-Linear Mechanics 37 2002 1147 1161 (Pubitemid 34405875)
    • (2002) International Journal of Non-Linear Mechanics , vol.37 , Issue.7 , pp. 1147-1161
    • Marynowski, K.1    Kapitaniak, T.2
  • 43
    • 34247399622 scopus 로고    scopus 로고
    • Zener internal damping in modelling of axially moving viscoelastic beam with time-dependent tension
    • DOI 10.1016/j.ijnonlinmec.2006.09.006, PII S0020746207000285
    • K. Marynowski, and T. Kapitaniak Zener internal damping in modeling of axially moving viscoelastic beam with time-dependent tension International Journal of Non-Linear Mechanics 42 2007 118 131 (Pubitemid 46628669)
    • (2007) International Journal of Non-Linear Mechanics , vol.42 , Issue.1 , pp. 118-131
    • Marynowski, K.1    Kapitaniak, T.2
  • 44
    • 5644274202 scopus 로고    scopus 로고
    • Steady state response of axially moving viscoelastic beams with pulsating speed: Comparison of two nonlinear models
    • L.Q. Chen, and X.D. Yang Steady state response of axially moving viscoelastic beams with pulsating speed: comparison of two nonlinear models International Journal of Solids and Structures 42 2005 37 50
    • (2005) International Journal of Solids and Structures , vol.42 , pp. 37-50
    • Chen, L.Q.1    Yang, X.D.2
  • 45
    • 33750309493 scopus 로고    scopus 로고
    • Vibration and stability of an axially moving viscoelastic beam with hybrid supports
    • L.Q. Chen, and X.D. Yang Vibration and stability of an axially moving viscoelastic beam with hybrid supports European Journal of Mechanics 25 2006 996 1008
    • (2006) European Journal of Mechanics , vol.25 , pp. 996-1008
    • Chen, L.Q.1    Yang, X.D.2
  • 46
    • 70449651522 scopus 로고    scopus 로고
    • Dynamic stability in parametric resonance of axially accelerating viscoelastic Timoshenko beams
    • L.Q. Chen, Y.Q. Tang, and C.W. Lim Dynamic stability in parametric resonance of axially accelerating viscoelastic Timoshenko beams Journal of Sound and Vibration 329 2010 547 565
    • (2010) Journal of Sound and Vibration , vol.329 , pp. 547-565
    • Chen, L.Q.1    Tang, Y.Q.2    Lim, C.W.3
  • 47
  • 48
    • 50549101850 scopus 로고    scopus 로고
    • Stability of axially accelerating viscoelastic beams: Multi-scale analysis with numerical confirmations
    • H. Ding, and L.Q. Chen Stability of axially accelerating viscoelastic beams: multi-scale analysis with numerical confirmations European Journal of Mechanics - A/Solids 27 2008 1108 1120
    • (2008) European Journal of Mechanics - A/Solids , vol.27 , pp. 1108-1120
    • Ding, H.1    Chen, L.Q.2
  • 49
    • 38249021949 scopus 로고
    • Vibration analysis of viscoelastic beams by separation of variables and modal analysis
    • D.J. Inman Vibration analysis of viscoelastic beams by separation of variables and modal analysis Mechanics Research Communications 16 1989 213 218
    • (1989) Mechanics Research Communications , vol.16 , pp. 213-218
    • Inman, D.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.