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Eigenvector analysis can be performed to determine the shapes and frequencies of the undampened free vibration modes of a system. These natural modes provide excellent insight into the behavior of a particular structure. Eigen vector analysis involves solving the generalized eigenvalue problem, which considers the stiffness and mass matrix of a structure. When a geometric nonlinear study must be performed, a situation that commonly occurs in the analysis of slender structures, nonlinear analysis or a more complete and rigorous evaluation that considers both parts of the total matrix is required. For instance, slender structures possess a small first frequency of vibration, less than 1 Hz, and can resonate due to wind excitation. The first frequency and shape of vibration are the most important parameters for calculating the response of a structure to environmental excitation. Therefore, when modal analysis depends on the stiffness of the structure, the effect of a reduction in stiffness on the modal shape of vibration must be determined. To this end, case studies were evaluated using the finite element method (FEM), considering and neglecting the geometric portion of the stiffness matrix. Mathematic functions were also applied for comparison.

Modal Shape, Geometric Stiffness, Nonlinear Analysis, Computational Simulation, Mathematic functions, Case Studies