Frequency Solutions with Contact

An important capability available in ADINA is that frequencies and mode shapes can be computed in nonlinear analysis. These analyses may contain geometric and material nonlinear conditions including contact, and the frequencies and mode shapes can be obtained at any solution step of the nonlinear analysis. The calculation can be performed using the subspace iteration method or the Lanczos method.

Here we give the frequency solutions obtained in two problems. Figure 1 shows the model of a bracket and also the areas of possible contact. The bracket is held together by a bolt.

Figure 1  Model of bracket showing contact surfaces (blue)

The lowest frequencies with and without frictional contact, and bolt tightening, are listed in Table 1. Note that without enforcing contact, that is, the bolt is present but not tightened, there are three rigid body modes. Of course, the frequencies are quite different when the bolt is tightened and contact is enforced, as it should physically be. The movie above shows the lowest vibration mode with contact enforced.

 TABLE 1  Frequencies of bracket with and without tightening ofbolt/contact conditions enforced

 Freq. No. Freq. (rad/s) With contact conditions Without contact conditions 1 0.3513E+05 0.1000E-04 2 0.3613E+05 0.1000E-04 3 0.6003E+05 0.1000E-04 4 0.7959E+05 0.8555E+04 5 0.9622E+05 0.1811E+05 6 0.1065E+06 0.2392E+05

Figure 2 shows a wheel, assembled with bolts. Similar observations hold for this analysis.

Figure 2  First vibration mode of the wheel — results for bolted wheel assembly (left)
and unbolted wheel assembly (right)

 TABLE 2  Frequencies for bolted and unbolted wheel assembly

 Freq. No. Freq. (rad/s) Bolted wheel assembly Unbolted wheel assembly 1 0.4998E+03 0.1000E-04 2 0.5057E+03 0.1000E-04 3 0.7031E+03 0.1000E-04 4 0.9888E+03 0.2357E+03 5 0.1019E+04 0.2360E+03 6 0.1023E+04 0.2843E+03

The capability of calculating frequencies and mode shapes at any step of a nonlinear analysis is clearly a very important and useful feature in ADINA.

Keywords:
Frequency analysis, contact, bolt, ADINA, nonlinear finite element, subspace iteration method, Lanczos method