zbMATH — the first resource for mathematics

A continuous approach to the aeroelastic stability of suspended cables in 1 : 2 internal resonance. (English) Zbl 1229.74067
Summary: This paper proposes a continuous perturbation treatment of the nonlinear equations of a cable, which is characterized by possible aeroelastic instability and internal resonance conditions. The objective is to evaluate the influence of stable modes (called passive) usually ignored when discretizing the model. The first step concerns the description of the structural equilibrium path under the action of the mean wind forces. Then, a multiple scale perturbation analysis of the integro-differential equations of motion is performed. Analyzing the stability of the reduced system, the existence of some limit cycles and of successive bifurcations is investigated. The comparison with previous papers, developed in the discrete field, allows clarification of the actual influence of the static equilibrium path and the contribution of passive modes.

74H55 Stability of dynamical problems in solid mechanics
74H60 Dynamical bifurcation of solutions to dynamical problems in solid mechanics
Full Text: DOI
[1] Blevins, R.D., Flow-induced Vibration, 2. ed. (1990) · Zbl 0385.73001
[2] Irvine, H.M., Cable Structures (1981)
[3] Lacarbonara, W., Proceedings of 2005 ASME Design Engineering Technical Conferences, DECT’05
[4] Lee, C.L., Nonlinear Dynamics 3 pp 465– (1992)
[5] Luongo, A., Journal of Sound and Vibration 214 (5) pp 915– (1998) · doi:10.1006/jsvi.1998.1583
[6] Luongo, A., Paolone, A., and Di Egidio, A., 2003, ”Computational problems in multiple scale analysis ,” in Recent Research Developments in Structural Dynamics , A. Luongo (ed.), Research Signpost, India, pp. 1–31. · Zbl 1041.70019
[7] Luongo, A., Journal of Sound and Vibration 288 (4) pp 1027– (2005) · doi:10.1016/j.jsv.2005.01.056
[8] Luongo, A., Journal of Mechanics of Materials and Structures 2 (4) pp 675– (2007) · doi:10.2140/jomms.2007.2.675
[9] Martinelli, L., Proceedings of 2nd International Conference on Structural Engineering, SEMC 2004
[10] Novak, M., ASCE 95 pp 115– (1969)
[11] Pakdemirli, M., Dynamics 8 pp 65– (1995)
[12] Piccardo, G., Journal of Wind Engineering and Industrial Aerodynamics 48 pp 241– (1993) · doi:10.1016/0167-6105(93)90139-F
[13] Rega, G., International Journal of Non-Linear Mechanics 34 pp 901– (1999) · Zbl 1068.74562 · doi:10.1016/S0020-7462(98)00065-1
[14] Steindl, A., International Journal of Solids and Structures 38 pp 2131– (2001) · Zbl 1003.74032 · doi:10.1016/S0020-7683(00)00157-8
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.