The eigenvalues of a partially embedded flexural, prismatic column

Abstract

AbstractMotivated from a large number of transmission and distribution utility poles that experience excessive vibrations during wind storms, this paper presents the eigenvalue analysis of a partially embedded flexural, prismatic column with ' length, , and exposed length, , and accounts for the interaction with the soil of its embedded portion. The study shows that the dynamics of a partially embedded prismatic column depend solely on the embedment ratio, and a dimensionless stiffness that expresses the relative stiffness between the soil surrounding the embedded length (level of fixity) and the exposed portion of the flexural column. A partially embedded prismatic column exhibits a finite number of eigenmodes that are lower than its rigid‐body mode, while the associated eigenfrequencies are lower than the corresponding eigenfrequencies of the fixed‐end cantilever (fec). For a typical value of the embedment ratio 0.15, the paper uncovers that for any eigenmode , of the fec, the partially embedded, prismatic column exhibits eigenmodes. The appearance of this additional eigenmode/eigenvalue happens invariably for any embedment ratio due to soil–structure interaction and is associated with the way that the flexural patterns of the partially embedded column emerge from the ground. The paper shows that the additional eigenmode/eigenvalue of the partially embedded column is also predicted with open‐source and commercially available finite‐element software.