Coupled String-Beam Equations as a Model of Suspension Bridges

Abstract

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A Mathematical Model of Suspension Bridges

“…The disadvantage of this principle consists in the fact that its application requires a rather restrictive assumption on the parameters fc, rai, 7712, 61, 62, E, I,T and the conditions obtained are too restrictive and are not satisfied by the real values of the bridge parameters. P. Drabek, H. Leinfelder and G. Tajcova [4] have established the existence of a unique time-periodic solution near stationary equilibrium under rather general assumptions on the above mentioned parameters, provided the external time-periodic forcing terms are small in a certain sense.…”

Torsional asymmetry in suspension bridge systems

“…Moreover, u 0 , θ 0 satisfy the boundary conditions (9). The functions u(t), θ(t) are a solution to the third dynamic problem D 3 if they satisfy the relations h r (u(t) − Dθ(t)) = h l (u(t) − Dθ(t)) = h(u(t) + Dθ(t)) = 0 for all t, the boundary conditions (8), and the variational equation (7). The variational equation (7) holds for all v, ϕ which satisfy the relations…”

“…The same model was numerically studied in [10] for some concrete parameters which corresponded to the original Tacoma bridge and some other suspension bridges. A different model of the central span was presented in [26] and [8], where the main cable was modeled as a string and the central span as a beam. The hangers were studied as a nonlinear continuum with the same properties as in the previous model.…”

Nonlinear Models of Suspension Bridges: Discussion of the Results

“…The proof for model (SB 1 ) can be found in [10], for model (SB 2 ) in [12] (here the proofs are based on the degree theory). The existence result for model (SB 2 ) is also proved in [27] (but there the author uses Galerkin method of approximative solutions).…”