[en] Vibrations of cables with a small bending stiffness concerns many engineering applications such as the fatigue assessment of stay cables. With the finite element (FE) method, the analysis can be performed with nonlinear truss elements, but bending effects are not taken into account. Otherwise, beam elements can be used, but the smallness of the bending stiffness may lead to numerical instability and mediocre results in boundary regions.
In this context, the paper presents an alternative method to calculate the time evolution of the profile of bending moments in boundary layers of cables, avoiding heavy FE analysis. The developments combine the theory of vibrations of extensible rods with asymptotic methods. The equations are decoupled between the slow dynamics of the boundary regions and the fast dynamics of the span. Then, a composite solution is constructed by means of a matched asymptotic procedure.
Disciplines :
Civil engineering
Author, co-author :
Canor, Thomas ; Université de Liège - ULiège > Département ArGEnCo > Analyse sous actions aléatoires en génie civil
Denoël, Vincent ; Université de Liège - ULiège > Département ArGEnCo > Analyse sous actions aléatoires en génie civil
Language :
English
Title :
Vibrations of cables with bending stiffness by an asymptotic approach
Publication date :
September 2013
Event name :
Fifth International Conference on Structural Engineering, Mechanics & Computation, SEMC2013
Event organizer :
University of Cape Town
Event place :
Cape Town, South Africa
Event date :
1-4 September 2013
Audience :
International
Main work title :
Fifth International Conference on Structural Engineering, Mechanics & Computation, Cape Town, 1-4 September 2013
Antman, S. (2005). Nonlinear Problems of Elasticity (2nd ed.). Applied Mathematical Sciences. Springer-Verlag.
Bernoulli, J. (1694). Curvatura laminae elasticae. Acta Eruditorum 13, 262-275.
Clough, R.W. & J. Penzien (1993). Dynamics of structures (2nd ed.). New-York: McGraw-Hill.
Coleman, B. D., E. H. Dill, M. Lembo, Z. Lu, & I. Tobias (1993). On the dynamics of rods in the theory of kirchhoff and clebsch. Archive Rational Mechanics Analysis 121, 339-359.
Denoël, V. & T. Canor (2013). Patching asymptotics solution of a cable with a small bending stiffness. Journal of Structural Engineering - ASCE 139, 180-187.
Denoël, V. & E. Detournay (2010). Multiple scales solution for a beam with a small bending stiffness. Journal of Engineering Mechanics 136(1), 69-77.
Hinch, E. (1991). Perturbation Methods, Volume 1. Cambridge: Cambridge University Press.
Impollonia, N., G. Ricciardi, & F. Saitta (2011). Vibrations of inclined cables under skew wind. International Journal of Non-Linear Mechanics 46(7), 907-918.
Lacarbonara, W. &A. Pacitti (2008). Nonlinear modeling of cables with flexural stiffness. Mathematical Problems in Engineering 2008.
Pellicano, F. & F. Zirilli (1998). Boundary layers and nonlinear vibrations in an axially moving beam. International Journal of Non-Linear Mechanics 33(4), 691-711.
Ricciardi, G. & F. Saitta (2008).A continuous vibration analysis model for cables with sag and bending stiffness. Engineering Structures 30(5), 1459-1472.
Stump, D. M.&W.B. Fraser (2000). Bending boundary layers in a moving strip. Nonlinear Dynamics 21(1), 55-70.
Stump, D. M. & G. H. M. van der Heijden (2000). Matched asymptotic expansions for bent and twisted rods: Applications for cable and pipeline laying. Journal of Engineering Mathematics 38(1), 13-31.
Warnitchai, P., Y. Fujino, & T. Susumpow (1995). A nonlinear dynamic model for cables and its application to a cablestructure system. Journal of Sound and Vibration 187, 695-712.
