4. Linear 1 DOF system

The one degree of freedom system is modeled with a single linear rod element, clamping one node and constraining all degrees of freedom of the other node except one. The material is linear elastic, and the mass of the rod is concentrated at the nodes and formulated by means of PMASS elements.

The theoretical solution is, for the case with initial displacement:

y t = d 0 cos ω t

with

ω = A E m L

where A is the rod cross section area, E the modulus of elasticity, m the mass per unit length, L the length of the rod, and d 0 is the initial displacement.

The test runs include a case with initial displacement only, one with a sine force, and one with gravity. Both the direct transient integration with B2000++ and modal transient analysis are checked.

One DOF model: Displacement response for initial displacement and large time step (multi step integration order 2).

Figure 78. One DOF model: Displacement response for initial displacement and large time step (multi step integration order 2).