Element Equations Of Motion Research Articles

The Dynamics of Rotor-Bearing Systems With Axial Torque—A Finite Element Approach

This study investigates the effect of constant axial torque on the dynamics of rotorbearing systems using a finite element model. The finite element equation of motion is formulated using the variational approach and the inclusion of axial torques gives rise to an incremental torsional stiffness matrix. This matrix is circulatory since the system is non-conservative. The finite element model is used to determine the static buckling torques and the critical speeds of a uniform shaft for short and long bearings.

Dynamic Response of Nonlinear Media at Large Strains

A finite element formulation is presented to treat the two-dimensional (plane or axisymmetric) response of elastic-plastic media to dynamic loadings including the effects of finite strains and rotations. The material constitutive laws are written in incremental fashion in terms of frame indifferent quantities, and applied to materials undergoing large deformations due to impulsive loadings. As an example, the Prandtl-Reuss relations are extended to include the effects of finite strains and included in developing the finite element equations of motion. Numerical results are presented for dynamic loading of a ring-reinforced tube subjected to internal blast loadings, dynamic forming of a flat circular plate against a parabolic die, and impact of an ogive projectile impinging against a flat rigid plate.