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.

本研究提出了一种评估具有复杂几何形状的薄壁梁在渐进压缩载荷下的振动和屈曲的有效方法。为了研究压缩载荷对薄壁梁的固有频率的影响，进行了一项综合研究。即，本研究提供了振动相关技术的数值模拟。有限元 (FE) 建立在 Carrera 统一公式 (CUF) 的框架中，薄壁梁复杂几何形状的位移使用低阶到高阶泰勒和拉格朗日多项式进行评估。结果与现有文献的实验结果和壳模型的数值结果进行了比较。还比较了由于振动模式引起的梁的横截面变形，并强调了能够准确检测复杂横截面变形的结构理论的重要性。获得的结果被证明是有前途和准确的，并且与实验和壳模型相当匹配，与这里提出的高效 CUF 相比，在计算成本方面更昂贵。