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Volumn 120, Issue 2, 1998, Pages 434-440

Study of the oscillations of a nonlinearly supported string using nonsmooth transformations

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; MATHEMATICAL TRANSFORMATIONS; NONLINEAR SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; STIFFNESS;

EID: 0032051214     PISSN: 10489002     EISSN: 15288927     Source Type: Journal    
DOI: 10.1115/1.2893848     Document Type: Article
Times cited : (15)

References (31)
  • 1
    • 24244444170 scopus 로고
    • Absence of Diffusion in Certain Random Lattices
    • Anderson, P. W., 1958, “Absence of Diffusion in Certain Random Lattices,” Physical Review, Vol. 109, pp. 1492-1505.
    • (1958) Physical Review , vol.109 , pp. 1492-1505
    • Anderson, P.W.1
  • 2
    • 0030258480 scopus 로고    scopus 로고
    • Localized and Nonlocalized Nonlinear Normal Modes in a Multi-span Beam With Geometric Nonlinearities
    • Aubrecht, J., and Vakakis, A. F., 1996, “Localized and Nonlocalized Nonlinear Normal Modes in a Multi-span Beam With Geometric Nonlinearities,” ASME JOURNAL OF VIBRATION AND ACOUSTICS, Vol. 118, No, 4, pp. 533-542.
    • (1996) ASME JOURNAL OF VIBRATION AND ACOUSTICS , vol.118 , Issue.4 , pp. 533-542
    • Aubrecht, J.1    Vakakis, A.F.2
  • 3
    • 0008205808 scopus 로고
    • Axisymmetric Elastic Wave Propagation in Weakly Coupled Layered Media of Infinite Radial Extent
    • Cetinkaya, C., Vakakis, A. F., and El-Raheb, M., 1995, “Axisymmetric Elastic Wave Propagation in Weakly Coupled Layered Media of Infinite Radial Extent,” J. Sound Vib., Vol. 182, No. 2, pp. 283-302.
    • (1995) J. Sound Vib. , vol.182 , Issue.2 , pp. 283-302
    • Cetinkaya, C.1    Vakakis, A.F.2    El-Raheb, M.3
  • 4
    • 0018446133 scopus 로고
    • Harmonic Wave Propagation in a Periodically Layered Infinite Elastic Body: Plane Strain, Analytical Results
    • Delph, T. J., Herrmann, G., and Kaul, R. K., 1979, “Harmonic Wave Propagation in a Periodically Layered Infinite Elastic Body: Plane Strain, Analytical Results,” ASME J. Appl. Mech., Vol. 46, pp. 113-119.
    • (1979) ASME J. Appl. Mech. , vol.46 , pp. 113-119
    • Delph, T.J.1    Herrmann, G.2    Kaul, R.K.3
  • 5
    • 0019062988 scopus 로고
    • Harmonic Wave Propagation in a Periodically Layered Infinite Elastic Body: Plane Strain, Numerical Results
    • Delph, T. J., Herrmann, G., and Kaul, R. K., 1979, Harmonic Wave Propagation in a Periodically Layered Infinite Elastic Body: Plane Strain, Numerical Results, ASME J. Appl. Mech., Vol. 47, pp. 531-537.
    • (1979) ASME J. Appl. Mech. , vol.47 , pp. 531-537
    • Delph, T.J.1    Herrmann, G.2    Kaul, R.K.3
  • 7
    • 0017931569 scopus 로고
    • Response of Periodic Structures by Modal Analysis
    • Engels, R. C., and Meirovitch, L., 1978, “Response of Periodic Structures by Modal Analysis,” J. Sound Vib., Vol. 56, No. 4, pp. 481-493.
    • (1978) J. Sound Vib. , vol.56 , Issue.4 , pp. 481-493
    • Engels, R.C.1    Meirovitch, L.2
  • 9
    • 0000381294 scopus 로고
    • Kink, Breather, and Asymmetric Envelope or Dark Solitons in Nonlinear Chains
    • Flytzanis, N., Pnevmatikos, S., and Remoissenet, M., 1985, “Kink, Breather, and Asymmetric Envelope or Dark Solitons in Nonlinear Chains,” J. Phys. C: Solid State Physics, Vol. 18, pp. 4603-4620.
    • (1985) J. Phys. C: Solid State Physics , vol.18 , pp. 4603-4620
    • Flytzanis, N.1    Pnevmatikos, S.2    Remoissenet, M.3
  • 10
    • 0028443683 scopus 로고
    • A Method for Studying Waves With Spatially Localized Envelopes in a Class of Nonlinear Partial Differential Equations
    • King, M. E., and Vakakis, A. F., 1994, “A Method for Studying Waves With Spatially Localized Envelopes in a Class of Nonlinear Partial Differential Equations,” Wave Motion, Vol. 19, pp. 391-405.
    • (1994) Wave Motion , vol.19 , pp. 391-405
    • King, M.E.1    Vakakis, A.F.2
  • 11
    • 0003676253 scopus 로고
    • Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts
    • Kissel, G. J., 1987, “Localization in Disordered Periodic Structures,” Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts.
    • (1987) Localization in Disordered Periodic Structures
    • Kissel, G.J.1
  • 12
    • 0000483874 scopus 로고
    • Self-localization of Vibrations in a One-dimensional Anharmonic Chain
    • Kosevich, A. M., and Kovalev, A. S., 1975, “Self-localization of Vibrations in a One-dimensional Anharmonic Chain,” Soviet Physics-JETP, Vol. 40, No. 5, pp. 891-896.
    • (1975) Soviet Physics-Jetp , vol.40 , Issue.5 , pp. 891-896
    • Kosevich, A.M.1    Kovalev, A.S.2
  • 13
    • 0002083761 scopus 로고
    • Asymptotic Soliton-like Solutions of Equations With Small Dispersion
    • Maslov, V. P., and Omelianov, G. A., 1981, “Asymptotic Soliton-like Solutions of Equations With Small Dispersion,” Advances in Mathematical Sciences-Usp. Mat. Nuuk, Vol. 36, No. 3, pp. 63-126.
    • (1981) Advances in Mathematical Sciences-Usp. Mat. Nuuk , vol.36 , Issue.3 , pp. 63-126
    • Maslov, V.P.1    Omelianov, G.A.2
  • 14
    • 0016846111 scopus 로고
    • Wave Propagation and Natural Modes in Periodic Systems: I. Mono-coupled Systems
    • Mead, D. J., 1975a, “Wave Propagation and Natural Modes in Periodic Systems: I. Mono-coupled Systems,” J. Sound Vib., Vol. 40, No. 1, pp. 1-18.
    • (1975) J. Sound Vib. , vol.40 , Issue.1 , pp. 1-18
    • Mead, D.J.1
  • 15
    • 0016846112 scopus 로고
    • Wave Propagation and Natural Modes in Periodic Systems: II. Multi-coupled Systems With and Without Damping
    • Mead, D. J., 1975b, “Wave Propagation and Natural Modes in Periodic Systems: II. Multi-coupled Systems With and Without Damping,” J. Sound Vib., Vol. 40, No. 1, pp. 19-39.
    • (1975) J. Sound Vib. , vol.40 , Issue.1 , pp. 19-39
    • Mead, D.J.1
  • 16
    • 0023044381 scopus 로고
    • A New Method of Analyzing Wave Propagation in Periodic Structures; Applications to Periodic Timoshenko Beams and Stiffened Plates
    • Mead, D. J., 1986, “A New Method of Analyzing Wave Propagation in Periodic Structures; Applications to Periodic Timoshenko Beams and Stiffened Plates,” J. Sound Vib., Vol. 104, No. 1, pp. 9-27.
    • (1986) J. Sound Vib. , vol.104 , Issue.1 , pp. 9-27
    • Mead, D.J.1
  • 17
    • 0001885281 scopus 로고
    • Kink Dynamics in the Highly Discrete Sine-Gordon System
    • Peyrard, M., and Kruskai, M. D., 1984, “Kink Dynamics in the Highly Discrete Sine-Gordon System,” Physica D, Vol. 14, pp. 88-102.
    • (1984) Physica D , vol.14 , pp. 88-102
    • Peyrard, M.1    Kruskai, M.D.2
  • 18
    • 0022191004 scopus 로고
    • The Calculation of Strongly Nonlinear Systems Close to Vibration-impact Systems
    • Pilipchuk, V. N., 1985, “The Calculation of Strongly Nonlinear Systems Close to Vibration-impact Systems,” PMM, Vol. 49, No. 5, pp. 572-578.
    • (1985) PMM , vol.49 , Issue.5 , pp. 572-578
    • Pilipchuk, V.N.1
  • 19
    • 0002900162 scopus 로고
    • A Transformation for Vibrating Systems Based on a Non-smooth Periodic Pair of Functions
    • (in Russian)
    • Pilipchuk, V. N., 1988, “A Transformation for Vibrating Systems Based on a Non-smooth Periodic Pair of Functions,” Doklady AN Ukr. SSR, Ser. A, 4, pp. 37-40 (in Russian).
    • (1988) Doklady AN Ukr. SSR, Ser. A , vol.4 , pp. 37-40
    • Pilipchuk, V.N.1
  • 20
    • 0006174897 scopus 로고    scopus 로고
    • Study of a Class of Subharmonic Motions Using a Nonsmooth Temporal Transformation (NSTT)
    • Pilipchuk, V. N., Vakakis, A. F., and Azeez, M. A. F., 1997, “Study of a Class of Subharmonic Motions Using a Nonsmooth Temporal Transformation (NSTT),” Physica D, Vol. 100, pp. 145-164.
    • (1997) Physica D , vol.100 , pp. 145-164
    • Pilipchuk, V.N.1    Vakakis, A.F.2    Azeez, M.A.F.3
  • 22
    • 45949123979 scopus 로고
    • Quasi-continuous Spatial Motion of a Mass-spring Chain
    • Rosenau, P., 1987, “Quasi-continuous Spatial Motion of a Mass-spring Chain,” Physica D 27, pp. 224-234.
    • (1987) Physica D , vol.27 , pp. 224-234
    • Rosenau, P.1
  • 23
    • 0028378494 scopus 로고
    • Exponentially Small Splittings of Manifolds in a Rapidly Forced Duffing System
    • Vakakis, A. F., 1994, “Exponentially Small Splittings of Manifolds in a Rapidly Forced Duffing System,” J. Sound Vib Vol. 170 No. 1, pp. 119-129.
    • (1994) J. Sound Vib , vol.170 , Issue.1 , pp. 119-129
    • Vakakis, A.F.1
  • 24
    • 0027540079 scopus 로고
    • Mode Localization in a Class of Multi-Degree-of-Freedom Nonlinear Systems With Cyclic Symmetry
    • Vakakis, A. F., and Cetinkaya, C., 1993, “Mode Localization in a Class of Multi-Degree-of-Freedom Nonlinear Systems With Cyclic Symmetry,” SIAM J. Appl. Math., Vol. 53, pp. 265-282.
    • (1993) SIAM J. Appl. Math. , vol.53 , pp. 265-282
    • Vakakis, A.F.1    Cetinkaya, C.2
  • 25
    • 0029133053 scopus 로고
    • Nonlinear Wave Transmission in a Monocoupled Elastic Periodic System
    • Vakakis, A. F., and King, M. E., 1995, “Nonlinear Wave Transmission in a Monocoupled Elastic Periodic System,” J. Acoust. Soc. Am., Vol. 98, No. 3, pp. 1534-1546.
    • (1995) J. Acoust. Soc. Am. , vol.98 , Issue.3 , pp. 1534-1546
    • Vakakis, A.F.1    King, M.E.2
  • 26
    • 0027606944 scopus 로고
    • A Multiple-seales Analysis of Nonlinear Localized Modes in a Cyclic Periodic System
    • Vakakis, A. F., Nayfeh, T., and King, M., 1993, “A Multiple-seales Analysis of Nonlinear Localized Modes in a Cyclic Periodic System,” ASME J. Appl. Mech., Vol. 60, No. 2, pp. 388-397.
    • (1993) ASME J. Appl. Mech. , vol.60 , Issue.2 , pp. 388-397
    • Vakakis, A.F.1    Nayfeh, T.2    King, M.3
  • 27
    • 0028425727 scopus 로고
    • Forced Localization in a Periodic Chain of Nonlinear Oscillators
    • Vakakis, A. F., King, M. E., and Pearlstein, A. J., 1994, “Forced Localization in a Periodic Chain of Nonlinear Oscillators,” Int. J. Non-linear Mech., Vol. 29, No. 3, pp. 429-447.
    • (1994) Int. J. Non-Linear Mech. , vol.29 , Issue.3 , pp. 429-447
    • Vakakis, A.F.1    King, M.E.2    Pearlstein, A.J.3
  • 29
    • 13644283366 scopus 로고
    • Periodic and Localized Waves in Vibro-impact Systems of Regular Configuration
    • Vedenova, E. G., and Manevich, L. I., 1981, “Periodic and Localized Waves in Vibro-impact Systems of Regular Configuration,” Mashinovedenie, Vol. 4, pp. 21-32.
    • (1981) Mashinovedenie , vol.4 , pp. 21-32
    • Vedenova, E.G.1    Manevich, L.I.2
  • 30
    • 0024089936 scopus 로고
    • Localization Phenomena in Mistuned Assemblies With Cyclic Symmetry: I: Free Vibrations, II: Forced Vibrations
    • Wei, S.-T., and Pierre, C., 1988, Localization Phenomena in Mistuned Assemblies With Cyclic Symmetry: I: Free Vibrations, II: Forced Vibrations, ASME JOURNAL OF VIBRATION, ACOUSTICS, STRESS AND RELIABILITY IN DESIGN, Vol. 110, pp. 429-448.
    • (1988) ASME JOURNAL OF VIBRATION, ACOUSTICS, STRESS AND RELIABILITY IN DESIGN , vol.110 , pp. 429-448
    • Wei, S.-T.1    Pierre, C.2
  • 31
    • 0011262051 scopus 로고
    • Periodic Nonlinear Waves on a Half-line
    • Weinstein, A., 1985, “Periodic Nonlinear Waves on a Half-line,” Commun. Math. Phys., Vol. 99, pp. 385-388.
    • (1985) Commun. Math. Phys. , vol.99 , pp. 385-388
    • Weinstein, A.1


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