The full linear theory for hinged beams with intermediate piers is developed. The analysis starts with the variational setting and the study of the linear stationary problem. Well-posedness results are provided and the possible loss of regularity, due to the presence of the piers, is analyzed. A complete spectral theorem is then proved, explicitly determining the eigenvalues according to the position of the piers and exhibiting the fundamental modes of oscillation. A related second-order eigenvalue problem is also studied, showing that it may display nonsmooth eigenfunctions and that the fourth-order problem cannot be seen as the square of a second-order problem.
Linear theory for beams with intermediate piers
Garrione M.;Gazzola F.
2020-01-01
Abstract
The full linear theory for hinged beams with intermediate piers is developed. The analysis starts with the variational setting and the study of the linear stationary problem. Well-posedness results are provided and the possible loss of regularity, due to the presence of the piers, is analyzed. A complete spectral theorem is then proved, explicitly determining the eigenvalues according to the position of the piers and exhibiting the fundamental modes of oscillation. A related second-order eigenvalue problem is also studied, showing that it may display nonsmooth eigenfunctions and that the fourth-order problem cannot be seen as the square of a second-order problem.File | Dimensione | Formato | |
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