Linear theory for beams with intermediate piers
2019 ◽
Vol 22
(08)
◽
pp. 1950081
◽
Keyword(s):
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.