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Coupled string-beam equations as a model of suspension bridges. (English) Zbl 1059.74522
The authors extend results of a recent paper by G. Tajčová [Appl. Math., Praha 42, No. 6, 451–480 (1997; Zbl 1042.74535)] to a broader class of input parameters. A system of two nonlinear partial differential equations represents a model of forced vibration of a central span of a suspension bridge, i.e. of the roadbed connected with the main cable by a system of vertical stays. Using a fairly sophisticated functional analytical method, the authors prove (i) the existence of a solution for any square-integrable loading and (ii) the uniqueness of the solution and some regularity, provided the external forcing terms are small in a certain sense and the weight of the cable is sufficiently small in comparison with the weight of the roadbed.

74H45 Vibrations in dynamical problems in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
74H20 Existence of solutions of dynamical problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
Full Text: DOI EuDML
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