6533b82bfe1ef96bd128ce58
RESEARCH PRODUCT
Steady states and nonlinear buckling of cable-suspended beam systems
Ivana BochicchioClaudio GiorgiElena Vuksubject
Perturbation (astronomy)010103 numerical & computational mathematicsBiparametric resonance; Cable-suspended beam; Nonlinear oscillations; Pitchfork bifurcation; Stationary solutions; Suspension bridgeCable-suspended beam01 natural sciencesBiparametric resonanceNonlinear oscillationssymbols.namesakeStationary solutions0101 mathematicsNonlinear bucklingNonlinear OscillationsPhysicsMechanical EngineeringPitchfork bifurcationMechanicsCondensed Matter PhysicsSuspension bridge010101 applied mathematicsPitchfork bifurcationFourier transformBucklingMechanics of MaterialssymbolsAxial loadDimensionless quantitydescription
This paper deals with the equilibria of an elastically-coupled cable-suspended beam system, where the beam is assumed to be extensible and subject to a compressive axial load. When no vertical load is applied, necessary and sufficient conditions in order to have nontrivial solutions are established, and their explicit closed-form expressions are found. In particular, the stationary solutions are shown to exhibit at most two non-vanishing Fourier modes and the critical values of the axial-load parameter which produce their pitchfork bifurcation (buckling) are established. Depending on two dimensionless parameters, the complete set of resonant modes is devised. As expected, breakdown of the pitchfork bifurcations under perturbation is observed when a distributed transversal load is applied to the beam. In this case, both unimodal and bimodal stationary solutions are studied in detail. Finally, the more complex behavior occurring when trimodal solutions are involved is briefly sketched.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-07-19 |