{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T15:42:33Z","timestamp":1760888553688},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2011,6,19]],"date-time":"2011-06-19T00:00:00Z","timestamp":1308441600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Nonlinear Dyn"],"published-print":{"date-parts":[[2012,2]]},"DOI":"10.1007\/s11071-011-0104-5","type":"journal-article","created":{"date-parts":[[2011,6,18]],"date-time":"2011-06-18T13:28:15Z","timestamp":1308403695000},"page":"1761-1778","source":"Crossref","is-referenced-by-count":3,"title":["On the predictability of elasto-plastic and geometrically non-linear oscillations of beams under harmonic excitation"],"prefix":"10.1007","volume":"67","author":[{"given":"P.","family":"Ribeiro","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,6,19]]},"reference":[{"key":"104_CR1","volume-title":"Nonlinear Oscillations","author":"A.H. Nayfeh","year":"1979","unstructured":"Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley, New York (1979)"},{"key":"104_CR2","volume-title":"Mechanical Metallurgy","author":"G.E. Dieter","year":"1986","unstructured":"Dieter, G.E.: Mechanical Metallurgy. McGraw-Hill, New York (1986)"},{"key":"104_CR3","volume-title":"Inelastic Analysis of Solids and Structures","author":"M. Koji\u0107","year":"2005","unstructured":"Koji\u0107, M., Bathe, K.-J.: Inelastic Analysis of Solids and Structures. Springer, Berlin (2005)"},{"key":"104_CR4","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1115\/1.3169093","volume":"52","author":"P.S. Symonds","year":"1985","unstructured":"Symonds, P.S., Yu, T.X.: Counter-intuitive behavior in a problem of elastic-plastic beam dynamics. ASME J. Appl. Mech. 52, 517\u2013522 (1985)","journal-title":"ASME J. Appl. Mech."},{"key":"104_CR5","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1115\/1.2894033","volume":"59","author":"J.-Y. Lee","year":"1992","unstructured":"Lee, J.-Y., Symonds, P.S., Borino, G.: Chaotic responses of a two-degree-of freedom elastic-plastic beam model to short pulse loading. ASME J. Appl. Mech. 59, 711\u2013721 (1992)","journal-title":"ASME J. Appl. Mech."},{"key":"104_CR6","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1016\/j.ijsolstr.2003.09.048","volume":"41","author":"Y.M. Liu","year":"2004","unstructured":"Liu, Y.M., Ma, G.W., Li, Q.M.: Chaotic and asymmetrical beam response to impulsive load. Int. J. Solids Struct. 41, 765\u2013784 (2004)","journal-title":"Int. J. Solids Struct."},{"key":"104_CR7","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.ijmecsci.2004.12.005","volume":"47","author":"G.W. Ma","year":"2005","unstructured":"Ma, G.W., Liu, Y.M., Zhao, J., Li, Q.M.: Dynamic asymmetrical instability of elastic-plastic beams. Int. J. Mech. Sci. 47, 43\u201362 (2005)","journal-title":"Int. J. Mech. Sci."},{"key":"104_CR8","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/BF01833745","volume":"9","author":"V. Karagiozov","year":"1996","unstructured":"Karagiozov, V., Karagiozova, D.: Chaotic phenomena in the dynamic buckling of an elastic-plastic column under an impact. Nonlinear Dyn. 9, 265\u2013280 (1996)","journal-title":"Nonlinear Dyn."},{"key":"104_CR9","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/0020-7462(94)00035-9","volume":"30","author":"U. Lepik","year":"1995","unstructured":"Lepik, U.: Elastic-plastic vibrations of a buckled beam. Int. J. Non-Linear Mech. 30, 129\u2013139 (1995)","journal-title":"Int. J. Non-Linear Mech."},{"key":"104_CR10","doi-asserted-by":"crossref","first-page":"819","DOI":"10.1016\/0020-7683(85)90085-X","volume":"21","author":"F. Ziegler","year":"1985","unstructured":"Ziegler, F., Irschik, H.: Dynamic analysis of elastic-plastic beams by means of thermoelastic solutions. Int. J. Solids Struct. 21, 819\u2013829 (1985)","journal-title":"Int. J. Solids Struct."},{"key":"104_CR11","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/BF01175861","volume":"62","author":"H. Irschik","year":"1986","unstructured":"Irschik, H.: Biaxial dynamic bending of elastoplastic beams. Acta Mech. 62, 155\u2013167 (1986)","journal-title":"Acta Mech."},{"key":"104_CR12","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/BF01175721","volume":"69","author":"P. Fotiu","year":"1987","unstructured":"Fotiu, P., Irschik, H., Ziegler, F.: Forced vibrations of an elasto-plastic and deteriorating beam. Acta Mech. 69, 193\u2013203 (1987)","journal-title":"Acta Mech."},{"key":"104_CR13","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1016\/0020-7403(93)90029-T","volume":"35","author":"E. Manoach","year":"1993","unstructured":"Manoach, E., Karagiozova, D.: Dynamic response of thick elastic-plastic beams. Int. J. Mech. Sci. 35, 909\u2013919 (1993)","journal-title":"Int. J. Mech. Sci."},{"key":"104_CR14","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/s004190000116","volume":"71","author":"J. Gerstmayr","year":"2001","unstructured":"Gerstmayr, J., Holl, H.J., Irschik, H.: Development of plasticity and damage in vibrating structural elements performing guided rigid-body motions. Arch. Appl. Mech. 71, 135\u2013145 (2001)","journal-title":"Arch. Appl. Mech."},{"key":"104_CR15","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/S0020-7462(01)00052-X","volume":"38","author":"J. Gerstmayr","year":"2003","unstructured":"Gerstmayr, J., Irschik, H.: Vibrations of the elasto-plastic pendulum. Int. J. Non-Linear Mech. 38, 111\u2013122 (2003)","journal-title":"Int. J. Non-Linear Mech."},{"key":"104_CR16","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1023\/B:NODY.0000014557.32797.c1","volume":"34","author":"M. Dibold","year":"2003","unstructured":"Dibold, M., Gerstmayr, J., Irschik, H.: Biaxial vibrations of an elasto-plastic beam with a prescribed rigid-body rotation including the effect of stiffening. Nonlinear Dyn. 34, 147\u2013157 (2003)","journal-title":"Nonlinear Dyn."},{"key":"104_CR17","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/j.jsv.2009.03.009","volume":"325","author":"P. Ribeiro","year":"2009","unstructured":"Ribeiro, P., van\u00a0der Heijden, G.H.M.: Elasto-plastic and geometrically nonlinear vibrations of beams by the p-version finite element method. J. Sound Vib. 325, 321\u2013337 (2009)","journal-title":"J. Sound Vib."},{"key":"104_CR18","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1016\/j.compstruc.2004.03.037","volume":"82","author":"P. Ribeiro","year":"2004","unstructured":"Ribeiro, P.: Non-linear forced vibrations of thin\/thick beams and plates by the finite element and shooting methods. Comput. Struct. 82, 1413\u20131423 (2004)","journal-title":"Comput. Struct."},{"key":"104_CR19","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1006\/jsvi.1999.2193","volume":"224","author":"P. Ribeiro","year":"1999","unstructured":"Ribeiro, P., Petyt, M.: Non-linear vibration of beams with internal resonance by the hierarchical finite element method. J. Sound Vib. 224, 591\u2013624 (1999)","journal-title":"J. Sound Vib."},{"key":"104_CR20","doi-asserted-by":"crossref","first-page":"2696","DOI":"10.1002\/nme.1180","volume":"61","author":"P. Ribeiro","year":"2004","unstructured":"Ribeiro, P.: A p-version, first order shear deformation, finite element for geometrically non-linear vibration of curved beams. Int. J. Numer. Methods Eng. 61, 2696\u20132715 (2004)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"104_CR21","volume-title":"Nonlinear Analysis of Plates","author":"C.-Y. Chia","year":"1980","unstructured":"Chia, C.-Y.: Nonlinear Analysis of Plates. McGraw-Hill, New York (1980)"},{"key":"104_CR22","doi-asserted-by":"crossref","first-page":"1927","DOI":"10.1088\/0022-3727\/8\/16\/003","volume":"8","author":"T. Kaneko","year":"1975","unstructured":"Kaneko, T.: On Timoshenko\u2019s correction for shear in vibrating beams. J. Phys. D, Appl. Phys. 8, 1927\u20131936 (1975)","journal-title":"J. Phys. D, Appl. Phys."},{"key":"104_CR23","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1006\/jsvi.2001.3634","volume":"246","author":"P. Ribeiro","year":"2001","unstructured":"Ribeiro, P.: Hierarchical finite element analyses of geometrically non-linear vibration of beams and plane frames. J.\u00a0Sound Vib. 246, 225\u2013244 (2001)","journal-title":"J.\u00a0Sound Vib."},{"key":"104_CR24","series-title":"National Bureau of Standards Applied Mathematics Series","volume-title":"Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables","year":"1972","unstructured":"Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards Applied Mathematics Series, vol.\u00a055. National Bureau of Standarts, Washington (1972)"},{"key":"104_CR25","volume-title":"Finite Element Procedures","author":"K.J. Bathe","year":"1996","unstructured":"Bathe, K.J.: Finite Element Procedures. Prentice Hall, New York (1996)"},{"key":"104_CR26","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1006\/jsvi.2000.3434","volume":"243","author":"M.I. McEwan","year":"2001","unstructured":"McEwan, M.I., Wright, J.R., Cooper, J.E., Leung, A.Y.T.: A combined modal\/finite element analysis technique for the dynamic response of a non-linear beam to harmonic excitation. J. Sound Vib. 243, 601\u2013624 (2001)","journal-title":"J. Sound Vib."},{"key":"104_CR27","volume-title":"Practical Bifurcation and Stability Analysis: From Equilibrium to Chaos","author":"R. Seydel","year":"1994","unstructured":"Seydel, R.: Practical Bifurcation and Stability Analysis: From Equilibrium to Chaos. Springer, Berlin (1994)"},{"key":"104_CR28","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/0167-2789(85)90011-9","volume":"16","author":"A. Wolf","year":"1985","unstructured":"Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a time series. Physica D 16, 285\u2013317 (1985)","journal-title":"Physica D"},{"key":"104_CR29","volume-title":"Vibrations and Stability. Advanced Theory, Analysis, and Tools","author":"J.J. Thomsen","year":"2003","unstructured":"Thomsen, J.J.: Vibrations and Stability. Advanced Theory, Analysis, and Tools. Springer, Berlin (2003)"},{"key":"104_CR30","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.compscitech.2008.09.038","volume":"69","author":"P. Ribeiro","year":"2009","unstructured":"Ribeiro, P.: On the influence of membrane inertia and shear deformation on the geometrically non-linear vibrations of open, cylindrical, laminated clamped shells. Compos. Sci. Technol. 69, 176\u2013185 (2009)","journal-title":"Compos. Sci. Technol."},{"key":"104_CR31","doi-asserted-by":"crossref","first-page":"1407","DOI":"10.1016\/j.ijmecsci.2010.03.005","volume":"52","author":"P. Ribeiro","year":"2010","unstructured":"Ribeiro, P.: Free periodic vibrations of beams with large displacements and initial plastic strains. Int. J. Mech. Sci. 52, 1407\u20131418 (2010)","journal-title":"Int. J. Mech. Sci."}],"container-title":["Nonlinear Dynamics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11071-011-0104-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11071-011-0104-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11071-011-0104-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T04:54:04Z","timestamp":1559364844000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11071-011-0104-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6,19]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,2]]}},"alternative-id":["104"],"URL":"https:\/\/doi.org\/10.1007\/s11071-011-0104-5","relation":{},"ISSN":["0924-090X","1573-269X"],"issn-type":[{"value":"0924-090X","type":"print"},{"value":"1573-269X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,6,19]]}}}