Time-periodic oscillations in suspension bridges: existence of unique solutions

Periodic solutions of nonlinear vibrating beams

“…Then, necessarily, T 1 and T 2 are multiples of some T 0 and the solution is actually T 0 -periodic. In our case, this is excluded by Proposition 3.5(iii) and the fact that σ(−L ω ) ∩ [2,12] = ∅ for any ω = q ∈ Z + , q = 1,2,3,5.…”

“…Clearly, L ω is selfadjoint and has a compact partial inverse on ImL ω . For more details on abstract operators like beam operators, we refer to [2].…”

“…The characterization of the subspace Z k0 cannot be obtained in a similar way since now the underlying symmetries concern both variables x and t. Since only the case k 0 = 1 is actually used in this paper (see Theorem 3.6), we will give a proof just for this case (being really the crucial one). To do so, let Q 1 = (0,π) 2 and…”

“…Because of the sign of the nonlinearity, the set of interacting eigenvalues is now σ(−L ω ) ∩ [2,12]. To be more precise, the periods of the pairs of solutions are…”

Torsional asymmetry in suspension bridge systems

“…The analysis showed that the equation has at least two solutions. The same equation has been studied in many papers, for instance, in [14], [2], [3], [6], [7], [4], [5], and [12], where the authors analyzed the structure of periodic solutions and proved the multiplicity of solutions. The same model was numerically studied in [10] for some concrete parameters which corresponded to the original Tacoma bridge and some other suspension bridges.…”