An important role in the design of structure is represented by the buckling analysis. The loading and service conditions, in which structures usually work, may significantly afflict their equilibrium state. This aspect often forces the design engineers to perform an accurate buckling analysis, in order to calculate critical loads of the structure. In fact, this critical load causes a sudden change of the structure, leading to a radical decrease in the loadcarrying capability. For these reasons, buckling analysis of beam-columns has been widely investigated in the past and recent years.

One of the most important experimental technology to calculate the critical buckling load of structures if represented by the Vibration Correlation Technique (VCT). It allows determining equivalent boundary conditions and buckling load for several types of structures and its strength is represented by the fact that it is a non-destructive methodology: essentially, the stability loads were determined by interpolating, until singularity, the natural frequency of the structure subjected to progressive higher loadings, without reaching the instability point. VCT is already widely used for beam, plate and shell structures.

This paper intends to assess a numerical simulation of the experimental data needed for the Vibration Correlation Technique. The solution proposed is developed in the domain of the Carrera Unified Formulation (CUF), according to which theories of structures can degenerate into a generalized kinematics that makes use of an arbitrary expansion of the generalized variables. Moreover, in order to reproduce results obtained in an experimental way, when large displacement and rotations may occur, geometrical nonlineatities have been taken into account. Thus, a finite element approximation is used along with a path-following method to perform nonlinear analyses.

Different types of structures have been analyzed, made with metallic and composite materials, and some results are compared with others found in the VCT literature. Results show how this methodology can well evaluate the natural frequencies on the structure in a geometrical nonlinear framework, and so also the critical buckling load.

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