Linear theory for beams with intermediate piers

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.