FREE-VIBRATIONS OF SPATIAL RODS - A FINITE-ELEMENT ANALYSIS

In this paper, a general finite-element (FE) formulation has been developed for natural frequency analysis of spatial rod systems. Accordingly, the frequency analysis of spatially curved and pretwisted rods, with either constant or varying cross-section on distributed elastic or point supports has been carried out. First, an appropriate finite-element equation is developed utilizing the governing equations (equations of motion, kinematical relations and constitutive relations) of a spatial rod. The time-dependent governing equations are then solved to find the modal shapes as well as the natural frequencies of the discretized system. The master element, developed herein, comprises 12 degrees of freedom (six at each end) and contains the rigid body motion as well as the deformation modes. This element has the generality of embodying the special cases of prismatic, curved and pretwisted elements, both with either linear or constant curvature changes. To verify the formulations several numerical examples are presented.