Simple models for natural frequencies and mode shapes of towers supporting utilities

The objective of this paper is to demonstrate simple approximate methods of obtaining natural frequencies and mode shapes of towers supporting utilities. The structural system considered is a lattice tower with a mass at the top, the mass representing a utility mounted on the tower. Modal characteristics of the tower-mass model are at first obtained by employing a model order reduction technique, namely the lumped mass method. These characteristics are subsequently compared to the corresponding modal properties of the system, found by using finite element analysis (FEA). Results for the first few modes are presented and show close agreement. Owing to the fact that the fundamental mode of vibration mainly contributes to the response of a structure, the system is then approximated by a cantilever beam with a mass at its free end and the fundamental natural frequency and mode shape are extracted by analytical formulation. The fundamental mode properties of this approximated system are again compared to the FEA model, and the values are observed to be in close agreement.