Analytical investigation of torsional mode in symmetric and asymmetric systems with mass or stiffness eccentricity

Abstract

At the first glance, it seems that asymmetry in geometry, mass, and stiffness cause torsion, while there are systems in which, despite the symmetry in all these parameters, the transferred energy to the torsional mode is more than the translational mode. The main purpose of this research was to study the torsional mode of a symmetric system in terms of geometry, mass, and stiffness, then investigate the effect of mass eccentricity and stiffness eccentricity. This is a fundamental problem and its main applications are in the buildings, automobile industry, and offshore structures. Parametric calculations on the free vibration equation of a completely symmetric system show that in a system with the specific values of the aspect ratio and the stiffness ratio of two directions, torsion occurs in the second mode. The results of these calculations were presented as a two-dimensional curve. Similar calculations were made on systems with eccentricity and the results were presented as three-dimensional curves. Accordingly, the greater mass eccentricity or stiffness eccentricity is, the greater area in which torsion occurs in the second mode will be. In the case of systems with mass eccentricity, there is a small area in which torsion occurs in the first mode.