Longitudinal vibration analysis of straight bars using mixed finite element method

In this study, the longitudinal vibration movements of elastic bars have been investigated using the Gâteaux differential method and the functional analysis method with different boundary conditions. Bars with straight axis and variable cross-section have been investigated and the natural frequencies have been obtained. By obtaining the functionals by using Gâteaux differential the mixed finite element method have been used. In the mized finite element method beside replacements the normal forces also have been used. By the mixed finite element method the element matrices have been obtained on two-nodded straight axis bar and for the verifying the obtained numeric results, the similar works in the literature were scanned and their results compared.