Efficient CUF-based method for the vibrations of thin-walled open cross-section beams under compression

This study proposes an efficient method for the evaluation of vibrations and buckling in thin-walled beams with complex geometries subjected to progressive compressive loads. A comprehensive study is conducted in order to investigate the effects of compressive loads on the natural frequencies of the thin-walled beams. Namely, a numerical simulation of the Vibration Correlation Technique is provided in this study. Finite Elements (FEs) are built in the framework of the Carrera Unified Formulation (CUF), and the displacements of complex geometric shapes of the thin-walled beams are evaluated using low- to higher-order Taylor and Lagrange polynomials. The results are compared with the experimental results of the available literature and the numerical results by the shell models. The cross-sectional deformations of the beam due to the vibration modes are also compared, and the importance of structural theories capable of accurate detection of complex cross-sectional deformations is highlighted. The obtained results are demonstrated to be promising and accurate and match reasonably well with the experiments and shell models, which are more expensive in terms of computational costs compared to the efficient CUF ones proposed here.