Alexandre de Macêdo Wahrhaftig,

Alexandre de Macêdo Wahrhaftig,

Federal University of Bahia (UFBa), Brazil

Title: : The rayleigh method applied to a actual 30-m-high metalic pole


Alexander M. Wahrhaftig has a degree in Civil Engineering (1991), with a Master in Rehabilitation of Historic Heritage from the University of Las Palmas de Gran Canaria, Spain (1995) and PhD in Civil Engineering (Structures) from the Polytechnic School of USP, São Paulo (2008). He has occupied leadership positions on the execution of works and technical services. In the research area mainly is engaged in static, dynamic, experimental analysis of structures, having scientific papers and one book published. Awarded twice by UFBa for his achievements in the field of innovation in 2013 was honored by the Brazilian Association of Civil Engineers.


An analytical approach based on the Rayleigh method is adopted to calculate the first resonance frequency of a 30-m-high metallic mobile phone pole system, taking into account the geometric stiffness, which includes the concentrated forces along of the height, and the self-weight of the structure. That solution constitutes a geometric nonlinear analysis and can be used to linearize second order effects, important for slender systems, since these effects are include automatically on calculation, without any interactions. However, it is important to bear in mind that actual structures are more complex than simple systems such as beams and columns because the properties of actual structures vary with their length. The mast is manufactured in steel and for that all analysis consider linear behavior. For comparison, a finite element method (FEM)-based computer simulation is performed. First, the axial forces on each segment of the structure are compared. Then, under geometric nonlinearity, the vibration frequency of the fundamental mode is calculated analytically as well as the buckling critical load is dynamically defined. Finally, the structural stiffness is evaluated. The results of the analytical approach are found to differ slightly from those of the FEM-based model. An experimental investigation is carried out to verify that frequency under environment excitation disregarding the damping influence. Considering the historical importance of the Rayleigh method in the field of mechanical vibrations, this work sought its application to an actual structure, along with a comparison of the analytical results with the results obtained using modern computing methods.