The first frequency of cantilevered bars with geometric effect: a mathematical and experimental evaluation

Abstract

In engineering, a large number of structures may be modeled as cantilevers. Due to their intrinsic characteristics, some of these structures are sensitive to dynamic actions. Gusts of wind are dynamic excitations for which the fundamental frequency of vibration is an important factor when calculating the structural response. Modeling the effects of the axial force on the natural frequencies of a structure usually results in systems of differential equations that are not solvable from a practical engineering perspective. This article develops a simple mathematical expression for calculating the fundamental frequency of cantilevered structures, within small ranges, that considers the presence of an axial demand. This expression has been validated by dynamic laboratory testing.