Determination of the first natural frequency of vibration of a steel pole, under the effect of geometric nonlinearity, using optimization techniques / Determinação da primeira frequência natural de vibração de um pólo de aço, sob o efeito da não linearidade geométrica, utilizando técnicas de optimização

This work aims to find a procedure to obtain an alternative formulation that represents the first mode of vibration of slender steel poles considering the effect of geometric non-linearity, using the Reyleigh-Ritz method, trigonometric formulations with optimization techniques and a finite element mathematical model. The application was on an existing polygonal steel pole. In order to consider the geometric non-linearity in the calculation of the natural frequencies of the respective structure, the concept of initial stiffness, geometric stiffness and effective stiffness, computed by the Rayleigh method for vibration problems in mechanical systems, was used. So, to optimize the computational time to obtain the modal response in dynamic analysis of the described structure, without neglecting the precision of the results of a rigorous analysis with sophisticated methodologies, alternative formulations to those described in NBR 6123 (1988) will bepresented in this work.

Analytical Assessments of Deformations and Natural Frequencies of Transmission Line Supports

The purpose of the study is to derive analytical expressions for estimating the lower vibration frequency of the power line support truss flat models. The forces in the bars of statically determinate structures are determined by the method of cutting out nodes in a program written in the Maple symbolic mathematics language. To find deformations, the Maxwell-Mohr's formula is used under the assumption that all rods are elastic, and that the supports are modeled by rigid rods. It is supposed that the hinges are ideal, and the mass of the structure in the form of point loads is distributed over the truss nodes, and only horizontal load displacements are considered. In comparison with similar problem statements with analytical forms of solution, the present study takes into account the masses at all nodes of the structure. For two-sided estimation of the fundamental frequency, the methods of Dunkerley and Rayleigh are used. The coefficients of the formulas in the solutions obtained for trusses with different numbers of panels form sequences, the common terms of which from the solution of linear recurrent equations give the final formula for the frequency dependence on the number of panels. As a result of the study, formulas for deflection and estimation of the fundamental frequency of truss natural vibration depending on the number of panels and dimensions of the structure have been derived. The obtained formulas can be used in carrying out engineering analyses of power transmission line supports. The formulas for the deflection and frequencies of the studied trusses have a form simple and convenient for use (in particular, for assessing the accuracy of numerical solutions). The frequency obtained by the Rayleigh method is much closer to the fundamental natural frequency than its value estimated using the Dunkerley method.

Flexural-Torsional Vibration of Thin-Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

The present paper analyzes the vibration issue of thin-walled beams under combined initial axial load and end moment in two cases with different boundary conditions, specifically the simply supported-end and the laterally fixed-end boundary conditions. The analytical expressions for the first natural frequencies of thin-walled beams were derived by two methods that are a method based on the existence of the roots theorem of differential equation systems and the Rayleigh method. In particular, the stability boundary of a beam can be determined directly from its first natural frequency expression. The analytical results are in good agreement with those from the finite element analysis software ANSYS Mechanical APDL. The research results obtained here are useful for those creating tooth blade designs of innovative frame saw machines.

Defects Avoidance in E-commerce Projects using Rayleigh Method

With the advent of e-commerce business, many software providers have started developing e-commerce solutions. However, the emphasis has to be given on developing defect free e-commerce portals. The current work is produced based on quantitative analysis done on five e-commerce projects. The defect data (discovery, fix and regression) are fed into the development process of the subsequent projects that helped in preventing the similar defects. A data analysis is done using Rayleigh Method to estimate the number of latent defects which may seep to the customers. This enabled in reduction in the count of User Acceptance Test defects, in the projects developed subsequently there by greatly decreasing the cost of development.