Steady-state dynamic analysis of a vehicle body-in-white model

The accuracy of the natural frequencies computed by the AMS eigensolver is evaluated assuming that the natural frequencies computed by the Lanczos eigensolver are exact, and relative errors are shown in Figure 2. These errors are less than 1.6% at frequencies below the global cutoff frequency of 300 Hz. Below 150 Hz, the region of particular interest, the errors are less than 0.25% and the resonance peaks in the frequency response function are reasonably accurate.

The accuracy of the steady-state dynamics solutions is evaluated qualitatively by comparing the frequency response curves. The response curves are compared at two different output locations: a drive point node and a transfer point node.

Figure 3 shows the point inertance at node 840950; the curve labeled SSD DIRECT represents the direct-solution steady-state dynamic analysis procedure, the curve labeled SSD SP represents the subspace-based steady-state dynamic analysis procedure, the curve labeled SSD AMS represents the SIM-based steady-state dynamic analysis procedure, and the curve labeled SSD AMS RES represents the SIM-based steady-state dynamic analysis procedure with residual modes. The curves are almost indistinguishable for frequencies below 125 Hz. To improve the accuracy of the response functions, residual modes can be added to compensate for high-frequency truncation errors. Calculation of residual modes is requested in the AMS eigenvalue extraction step by specifying the nodal points where forces are applied. For this solution (SSD AMS RES), the global cutoff frequency is set to 225 Hz instead of 300 Hz to demonstrate that the global cutoff frequency can be lowered without losing accuracy. By lowering the global cutoff frequency to 225 Hz and adding two residual modes in the global eigenmode subspace, a speed up of approximately 25% can be achieved.

Figure 4 shows the transfer inertance at the node located at the bottom of the driver’s seat; the same curve labels discussed above are used in this figure. The frequency response computed by the SIM-based steady-state dynamic analysis procedure nearly matches those computed by the subspace-based steady-state dynamic analysis procedure and the direct-solution steady-state dynamic analysis procedure for the frequencies below 125 Hz. To improve accuracy for frequencies higher than 125 Hz, more eigenmodes should be extracted and used.

The overall performance comparison among the three steady-state dynamic analysis procedures is summarized in Table 1 (analysis cost is independent of whether or not residual modes are used). Performance was evaluated on a Linux/x86-64 server with a single processor. The amount of available memory was set to 16 GB for each run. It is clear that the SIM-based steady-state dynamic analysis procedure using the AMS eigensolver shows excellent performance compared to the subspace-based steady-state dynamic analysis procedure using the Lanczos eigensolver or the direct-solution steady-state dynamic analysis procedure.