SHALLOW ARCHES WITH WEAK AND STRONG DAMPING
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The paper develops a rigorous mathematical framework for the behavior of arch and membrane like structures. Our main goal is to incorporate moving point loads. Both the weak and the strong damping cases are considered. First, we prove the existence and the uniqueness of the solutions. Then it is shown that the solution in the weak damping case is the limit of the strong damping solutions, as the strong damping vanishes. The theory is applied to a car moving on a bridge.
Abstract
The paper develops a rigorous mathematical framework for the behavior of arch and membrane like structures. Our main goal is to incorporate moving point loads. Both the weak and the strong damping cases are considered. First, we prove the existence and the uniqueness of the solutions. Then it is shown that the solution in the weak damping case is the limit of the strong damping solutions, as the strong damping vanishes. The theory is applied to a car moving on a bridge.
참고문헌 (11)
- J. M. Ball, "Stability theory for an extensible beam", J. Differential Equations, 14, pp.399~418 (1973)
- J. S. Chen, "Effects of elastic foundation on the snap-through buckling of a shallow arch under a moving point load", Internat. J. Solids Structures, 43, pp.4220~4237 (2006)
- M. C. Cheung, "The static and dynamic stability of clamped shallow circular arche", Doctor, pp.1969
- E. Emmrich, "A class of integro-differential equations incorpo-rating nonlinear and nonlocal damping with applications in nonlinear elastodynamics:existence via time discretization", Nonlinearity, 24(9), pp.2523~2546 (2011)
- J. S. George, "Dynamic Stability of Suddenly Loaded Structures", pp.117~153 (1990), Springer Book
- P. Grisvard, "Singularities in Boundary Value Problems" (1992), Springer-Verlag
- S. Gutman, "Parameter identification for weakly damped shallow arches", J. Math. Anal. Appl, 403(1), pp.297~313 (2013)
- J. Ha, "Stability of shallow arches under constant load", Internat. J. Non-Linear Mechanics, 58, pp.120~127 (2014)
- N. J. Hoff, "Dynamic analysis of the buckling of laterally loaded flat arches", J. Math Phys, 32, pp.276~288 (1954)
- J. L. Lions, "Nonhomogeneous Boundary Value Problems nd Applica-tions" (1972), Springer
- R. Temam, "Infinite Dimensional Dynamical Systems in Mechanics and Physics" (1997), Springer-Verlag