Fundamental Vibration Periods of Continuous Beams with Two Unequal Spans

The analysis of the vibration of continuous beams was largely treated in the scientific literature by researchers using different methods. The objective of this study is to determinate the fundamental transverse vibration period T1 of two-span beams having an intermediate support of varying abscissa. Various boundary conditions at the extreme ends of the analyzed continuous beams are considered. The analysis was conducted by the finite element method based upon the Euler–Bernoulli assumptions. The transverse vibration period is calculated for each position of the intermediate support for different end restraints. The validations are relative to particular abscissas and extreme locations of the intermediate support. Accurate results are obtained in accordance with the theory. At the end, the obtained results for the analyzed beams are plotted as curves representing the variations of T1 as a function of the intermediate support location expressed by the ratio of the first span length over the total beam length.