Estudo comparativo entre métodos numérico e experimental de análise modal aplicada ao problema de vibração transversal de uma viga fixa-livre

• Main Author: Silva Filho, Silvio de Oliveira
• Publication Date: 2025
• Format: Bachelor thesis
• Language: por
• Source: Repositório Institucional da UTFPR (da Universidade Tecnológica Federal do Paraná (RIUT))
• Download full: http://repositorio.utfpr.edu.br/jspui/handle/1/36181
• topic: Acelerômetros; Análise modal; Vigas - Juntas; Accelerometers; Modal analysis; Girders - Joints; CNPQ::ENGENHARIAS::ENGENHARIA MECANICA

Vibration is the motion that repeats itself, either regularly or irregularly, after a time interval, and it can influence engineering projects and limit their performance. In structural projects, determining natural frequencies is crucial to avoiding the phenomenon of resonance, which can lead to significant increases in vibration amplitudes, resulting in severe structural damage. The natural frequencies and vibration modes of structures can be obtained through modal analysis. This study aims to understand the application of experimental and numerical methods in modal analysis. For this purpose, it is proposed to set up a test bench to study the transverse vibrations of a cantilever beam, which has an analytical solution, thus facilitating the validation of both the experimental and numerical methods. In the experimental method, an impact hammer is used to excite the beam transversely, generating acceleration measured over time by an axial accelerometer. The measurements, performed with the aid of LabVIEW, of force and acceleration in the time domain are converted to the frequency domain using the Fast Fourier Transform. The responses as a function of frequency are exported to Matlab, which is used to extract the transfer functions and natural frequencies. In turn, the numerical method consists of using Ansys to obtain the natural frequencies and transverse vibration modes of the beam. The numerical results are compared with the analytical solutions, while the experimental results are compared with the numerical results. To validate the calibration of the accelerometer and the impact hammer, an experiment is conducted to determine the natural frequencies of a free-free beam. As expected, the numerical results closely matched the analytical results. However, the experimental results presented unexpected errors, likely caused by the boundary conditions of the beam-frame assembly, which did not ensure zero displacement at the fixed support.