On the "Best" Mode Form in the Mode Approximation Technique Using the Finite Element Method

ABSTRACT A systematic procedure for choosing the “best” mode shape is discussed by extending the mode approximation technique. The finite element method is used to calculate several valid mode forms of a given structure. Nonlinear eigenvalue problems are solved by an iterative procedure in order to obtain mode forms. Since one can choose only one mode form in the mode approximation technique due to nonlinearity of viscoplastic materials, the lower bound theorem on final time is applied to identify the best mode form. The validity of the concept is demonstrated by numerical results from two example problems of clamped beam and portal frame.