Composite, mass proportional, and rotary inertia proportional damping in Abaqus/Standard

An eigenvalue analysis is performed on the system consisting of spring, mass, and rotary inertia elements. The spring element builds the stiffness for the translational degrees of freedom, while the mass is assigned to all six degrees of freedom (due to the mass and rotary inertia elements). To avoid solver singularities, a B31 element with negligible mass is included in the model. Composite damping values are also specified for both the mass and rotary inertia elements.

The linear behavior of a simple spring/mass system with mass proportional damping is tested (see system A in Linear behavior of spring and dashpot elements). The MASS element (m = 0.02588) is attached to a SPRING1 element; therefore, the system is grounded. The value of the mass proportional damping parameter ($\alpha$ = 4.6367852) was taken such that the damping in the system ($c=\alpha m$) is the same as in Problem I in Linear behavior of spring and dashpot elements when a dashpot element (c = 0.12) is used to provide damping.

The behavior of a simple spring/rigid body system with rotary inertia proportional damping is tested. A rigid body (one R2D2 element), with rotary inertia at its reference node and rotary inertia proportional damping, is allowed only rotation about the z-axis. The rotation of the rigid element is constrained by the two springs acting normal to it. In the first step the rigid body is rotated by 10° in a static procedure, thus developing forces in the springs. In the next dynamic step the above single degree of freedom system is allowed to oscillate freely. An additional perturbation step is included to test the load case definition.