Spectral analysis connected with suspension bridge systems. (English) Zbl 1333.74042
Summary: In this paper, three dynamic linear models of the main span of suspension bridges are studied. The models describe vertical and torsional oscillations of the deck under the action of lateral wind. The problems correspond to the situations when both the midspan cable bands are loosened, both the midspan bands are fixed, and one midspan band is fixed and the other is loosened. Three corresponding eigenvalue and eigenvector problems are formulated and analysed. The continuous dependence of eigenvalues and eigenvectors on data are proved. The analysis of the three eigenvalue and eigenvector problems against flutter is carried out, which reveals possible reasons of the collapse of the original Tacoma suspension bridge.
MSC:
74H45 | Vibrations in dynamical problems in solid mechanics |
74H55 | Stability of dynamical problems in solid mechanics |
74H10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics |