Vibration analysis of fixed-fixed prestressed beam using Tau and experimental methods

In this paper, numerical Tau method using Legendre and Chebyshev polynomial bases is proposed to extract the natural frequencies of fixed-fixed prestressed beams. To this end, the necessary formulations for the prestressed beam and the numerical Tau method are first established. A beam without tension is then tested to update the model parameters, with data acquisition performed using piezoelectric sensors and a laser vibrometer to extract its natural frequencies through experimental modal analysis. Additionally, by averaging the signal from the strain gauge installed on the beam, the initial strain in the model equations is estimated. To verify the accuracy of the results obtained using the numerical Tau method for different tensile forces, the beam is tested on a tensile testing machine. The natural frequencies are extracted for each tensile force, and the results are compared with those obtained from the numerical Tau method. These comparisons show an increase in natural frequencies as tensile forces increase. Moreover, the difference between the numerical and experimental results decreases significantly as the order of estimation in the functions increases. The frequency response functions of accelerance and mobility for different tonnages indicate a change and increase in frequency with increasing force, while the frequency amplitudes do not follow a specific pattern.