Vibration of an SDOF Representing a Rigid Beam Supported by Two Unequal Columns with One Mounted on a Flexible Base

The structural dynamic analysis considers a basic mechanical vibrating system to represent a single degree of freedom. Such a system commonly formed by an infinitely rigid beam supported by two columns is used to establish the dynamic equilibrium equation. The analyzed single degree of freedom noted 1-DOF in this contribution considers different heights for the columns while a torsion spring is disposed at the first column base. Thus, the lateral stiffness is constituted by the sum of the contributions of the first column, the torsional spring, and the second column. This study allowed the determination of the vibration period of the 1-DOF by using the finite element method for various heights ratios and different values of the torsion spring stiffness. The findings of the conducted investigations are presented on plotted curves giving the vibration period T as a function of both the heights ratio and the torsion spring stiffness value.