Numerical vibration correlation technique for thin-walled composite beams under compression based on accurate refined finite element

This paper investigates the virtual vibration correlation technique for the evaluation of the variations of the natural frequencies for highly flexible thin-walled composite beams. In this regard, refined finite element based on the Carrera Unified Formulation (CUF) is developed. Thin-walled composite beams with various cross-sections of box, I-shaped and channel-shaped types, are investigated. Additionally, a comparison of the CUF results with the implemented shell models and the available literature is presented in order to evaluate the accuracy and efficiency of the proposed method. It is indicated that classical beam theories such as Euler–Bernoulli and Timoshenko beam theories failed to have an accurate prediction of the natural frequencies and dynamic response of thin-walled beam structures. Therefore, the necessity of employing higher-order and refined beam theories capable of capturing cross-sectional deformations is highlighted. Furthermore, to fully demonstrate the capabilities of the CUF-1D method with efficient Lagrange expansion, a more complex structural problem of a channel-shaped composite beam with the different numbers of transverse stiffeners is studied, and conclusions about the buckling behavior and variations of natural frequencies are drawn. It is shown that the numerical assessments by the proposed efficient CUF method in this paper correlate well with the shell results which are more computationally expensive.