Flexural-torsional bifurcations of a cantilever beam under potential and circulatory forces II. Post-critical analysis

International Journal of Non-Linear Mechanics

Volumn 41, Issue 4, 2006, Pages 595-604

  Paolone, Achille ^a   Vasta, Marcello ^b   Luongo, Angelo ^c  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF CHIETI   (Italy)

^c UNIVERSITY OF L'AQUILA   (Italy)

Author keywords

Bifurcation analysis; Keldysh's eigenfunctions; Multiple scale method

Indexed keywords

BENDING STRENGTH; BIFURCATION (MATHEMATICS); BUCKLING; EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; NUMERICAL ANALYSIS;

BIFURCATION ANALYSIS; KELDYSH'S EIGENFUNCTIONS; MULTIPLE SCALE METHOD;

CANTILEVER BEAMS;

EID: 33748120905     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2006.02.004     Document Type: Article

References (17)

1. Langthjem M.A., and Sugiyama Y. Dynamic stability of columns subjected to follower loads: a survey. J. Sound Vib. 238 5 (2000) 809-851
2. A. Luongo, A. Di Egidio, A. Paolone, Multiple scale bifurcation analysis for finite-dimensional autonomous systems, Recent Research Developments in Sound and Vibration, vol. 1, Transworld Research Network, Kerala, India, 2002, pp. 161-201.
3. Luongo A., and Paolone A. Perturbation methods for bifurcation analysis from multiple nonresonant complex eigenvalues. Nonlinear Dyn. 14 (1997) 193-210
4. Luongo A., Di Egidio A., and Paolone A. Multiple time scale analysis for bifurcation from a multiple-zero eigenvalue. AIAA J. 41 6 (2003) 1143-1150
5. Luongo A., and Paolone A. Multiple scales analysis for divergence-Hopf bifurcation of imperfect symmetric systems. J. Sound Vib. 218 (1998) 527-539
6. A. Luongo, A. Paolone, M. Vasta, Bifurcation analysis of thin-walled beam under conservative and non-conservative loads, Fifth European Conference on Structural Dynamics EURODYN, Munich, Germany, 2002.
7. Luongo A., and Di Egidio A. Bifurcation equations through multiple-scales analysis for a continuous model of a planar beam. Nonlinear Dyn. 41 (2005) 171-190
8. Nayfeh A.H. Perturbation Methods (1973), Wiley, New York
9. Thompson J.M.T., and Hunt G.W. A General Theory of Elastic Stability (1973), Wiley, London
10. Iooss G., and Joseph D.D. Elementary Stability and Bifurcation Theory (1980), Springer, New York
11. Nayfeh A.H. Perturbation methods in nonlinear dynamics. In: Jowett J.M., Month M., and Turner S. (Eds). Topical Course on Nonlinear Dynamics, Società Italiana di Fisica, Santa Margherita di Pula (1985), Sardinia, Springer, Berlin
12. Kirillov O.N., and Seyranian A.P. Collapse of Keldysh chain and stability of nonconservative systems. Dokl. Math. 66 1 (2002) 127-131 (Translated from Dokl. Math. Nauk 385(2) (2002) 172-176)
13. Kirillov O.N., and Seyranian A.P. Solution to the Herrmann-Smith problem. Dokl. Phys. 47 10 (2002) 767-771 (from Dokl. Akad. Nauk 386(6) (2002) 761-766)
14. Keldysh M.V. On eigenvalues and eigenfunctions of certain classes of not self-adjoint equations. Dokl. Akad. Nauk SSSR 77 1 (1951) 11-14
15. Oden J.T., and Reddy J.N. Variational Methods in Theoretical Mechanics (1982), Springer, New York
16. Leipholz H. Direct Variational Methods and Eigenvalue Problems in Engineering (1975), Noordhoff, Leiden
17. Troger H., and Steindl A. Nonlinear Stability and Bifurcation Theory (1991), Springer, Wien, New York