For this simulation 30 modes were used to represent the dynamic behavior of the structure. The total modal effective mass for all of these modes was well over 90% of the mass of the structure that can move in the y- and z-directions, indicating that the dynamic representation is adequate.
Figure 1 shows the displacement in the direction of degree of freedom 2 of the node in set Tip-a versus time and illustrates the effect of using fewer modes on the quality of the results. If you look at the table of effective mass, you will see that the first significant mode in the 2-direction is mode 3, which accounts for the lack of response when only two modes are used. The displacement of this node in the direction of degree of freedom 2 for the analyses using five modes and 30 modes is similar after 0.2 seconds; however, the early response differs, suggesting that there are significant modes in the range of 5–30 relating to the early response. When five modes are used, the total modal effective mass in the 2-direction is only 57% of the moveable mass.
Figure 1. Effect of different numbers of modes on the results.
