Guyed Towers Dynamics Using Karhunen-Loeve Expansions

Abstract

The dynamics of a guyed tower is herein analyzed. The finite element model of a plane lattice tower is made of two-node truss elements fixed at its base. Two inclined, symmetrically arranged cables are alsomodeled with truss elements considering the lack of compression capacity of these elements. The tower is subjected to a transverse load (distributed along the height) that may be static or dynamic with a cosine temporal variation. Due to the intrinsic nonlinear behavior of this structural system, the analysis is carried out with a mechanical event simulation modulus of a finite element package. The gravity loads on the tower and cables and the initial pre-stressing of the cables are first applied until static equilibrium stabilizes. Then the load, either static or dynamic, is activated. Once the time history of the tower
displacements is obtained, a Karhunen-Loève (KL) decomposition (also known as Proper Orthogonal Decomposition, POD) is performed so as to obtain the proper orthogonal values (POV’s or Karhunen-Loève energy contributions) and the proper orthogonal modes (POM’s or Karhunen-Loève basis). The bases are optimal in the least squaremethod sense. The qualitative analysis of these results can give clues on the dynamic behavior of the structural system.. Furthermore, the KL bases are optimal to construct
a low reduced model, i.e. its use in a Galerkin’s approach is convenient since very few modes contain the larger information on the dynamics. As is known the proper orthogonal modes (POM’s) match the eigenmodes in the linear cases. If dealing with nonlinear cases as the present one, they contain additional information.