Análise de vibrações mecânicas em estruturas esbeltas e flexíveis, como cordas e vigas, sujeitas à movimentação axial utilizando a técnica da transformada integral generalizada

Abstract

The dynamic analysis of vibrations on flexible structures is of an extreme importance in engineering and its solution represents a significant challenge to be tackled. This study has the objective to investigate thin and flexible structures such as beams and ropes, that oscillate in supports clamped-clamped and clamped-concentrated mass, which determine the boundary conditions of the analysis problem. Using the generalized integral transformation technique (GITT) that converts the partial differential equation (PDE) developed by the Hamiltonian method in an Ordinary Differential Equation (ODE), it optimizes the numerical process andcontrols efficiently the relative error of the calculations. In this study, it was developed and applied an innovative method that treats the boundary conditions without the use of filters to homogenize the equations. The calculations methodology was implemented in Fortran, utilizing a sub-routine DIVPAG of IMSL. As reference, a thorough analysis of convergence and stableness was applied, considering the behavior of four different models of ropes and two models of beams. The validation of methodology was approached comparing functional aspects such as transversal displacement, system velocities, frequencies, and damping, with results obtained by GITT and other studies that applied the same simulation conditions. The results of this study were found to be satisfactory, which highlights the relevancy of application of this vibration analysis method. It was also assessed the application of this method in different vibration configurations in each model, which exemplifies its broad potential in problems involving the structures analyzed. Therefore, this study represents a significant contribution to the advance of knowledge in dynamic modeling of thin and flexible structures and highlights the influence of boundary conditions in vibrational characteristics of these structures.Furthermore, it introduces an innovative methodology for treating boundary conditions without the use of filters, expanding the analysis possibilities in this field of engineering.