Analysis of the First Modal Shape Using Two Case Studies

Eigenvector analysis can be performed to determine the shapes of the undamped free vibration modes of a system. Eigenvector analysis involves solving the generalized eigenvalue problem, which considers the stiffness and mass matrix of a structure. For a geometric nonlinear study, both parts of the total stiffness matrix are required. As modal analysis depends on the stiffness, the effect of its reduction on the modal shape of vibration of the structure must be determined. Case studies were evaluated using the finite element method, considering and neglecting the geometric portion of the stiffness matrix. Mathematic functions were applied for comparison.