22 Acoustic Cavity Modal Analysis for NVH Development of Road Machinery Cabins 223 Table 22.1 Comparison of acoustic modal frequencies nx Index ny nz Analytical mode (Hz) FEA mode (Hz) Test mode (Hz) Analytical FEA Analytical vs. test vs. test vs. FEA (%) 0 0 1 1 97:2 1 115:9 4 112:1 13:3 3.4 16.1 0 1 0 2 110:7 2 132:7 2 93:6 18:7 41.8 16.6 1 0 0 3 126:9 3 149:9 6 137:4 7:6 9.1 15.3 0 1 1 4 147:3 4 185:3 7 171:7 14:2 7.9 20.5 1 0 1 5 159:8 5 194:8 – – – 18.1 1 1 0 6 168:4 6 215:7 – – – 21.9 1 1 1 7 194:4 8 228:7 9 230:5 15:6 0.8 15.0 analytical solution, FEA and test. Note that the modal sequence achieved from test is quite different from the one predicted by analytical solution and FEA. For instance, the vertical mode (0, 0, 1) is the first mode in analytical solution and FEA but the fourth mode in test. Also, in test the vertical mode (0, 0, 1) comes after the lateral mode (0, 1, 0) whereas in analytical solution and FEA the sequence of these two modes is switched. In addition, the natural modes given by test are slightly lower compared to the FEA prediction. This is because the flexibility of panels surrounding the cavity results in an “elastic” acoustical boundary condition hence making the cavity acoustically longer than the physical dimensions [4]. For the cab in-situ, the side panels are made of glass whereas the roof and floor are steel, therefore the cavity wall is softer laterally but stiffer vertically, which makes the cavity acoustically longer in lateral direction (y-axis) than the vertical direction (z-axis). It is also noticed that modes (1, 0, 1) and (1, 1, 0) are missing in test, which is due to the elastic cavity wall as well. The prediction accuracy of analytical solution and FEA can be measured by the percentage discrepancy against experimental results. The accuracy level of anlytical prediction is between 80 and 90 % and the one of FEA prediction is as high as 90 % except for the 2nd mode (0, 1, 0) which has a 40 % predicting deviation. The mode shapes associated with Table 22.1 are plotted in Fig. 22.5. Note that FEA and test have a nearly perfect match for 1Dand 2Dmodes and a reasonable agreement for the first 3Dmode (1, 1, 1). It should be emphasized once again that the experimental modal sequence needs to be adjusted to match the counterpart mode shapes given by analytical solution and FEA. Besides, a fairly reasonable agreement is found between analytical solution and FEA, especially in the case of 1D and2Dmodes. This implies that the geometrical deviation between an FE model and its equivalent rectangular box is not so significant in predicting the lower order acoustic cavity mode shapes. Figure 22.6 depicts the unique testing modes that are not listed in Table 22.1. Note that the first mode in test is a longitudinal mode (1, 0, 0) at 79.7 Hz in x-axis, shown in Fig. 22.6a. The third testing mode shown in Fig. 22.6b is a quasivertical mode in z-axis meaning a transition mode between the 2nd lateral mode and the 4th vertical mode. Figure 22.6c, d present the modes in such a way that they can be somewhat treated as a (0, 0.5, 0.5) mode and a (1, 0.5, 0.5) mode, respectively. Again, these unique modes can be attributed to the vibro-acoustic coupling effect between the air cavity and the flexible cab panels. 22.5.2 Impact of the Seat and Steering Column on Experimental Acoustic Modal Parameters The addition of the seat and steering column introduces a mass coupling effect to the interior sound field which could generate a substantial impact on the cavity acoustic behaviors [8]. Table 22.2 shows the acoustical natural frequencies and modal damping that were extracted from measurements with and without the addition of the seat and steering column. The first observation is that the modal frequencies are uniformly shifted downwards by 1–5 % after adding the seat and steering column. Particularly, the vertical mode #4 shifts more to the lower value than the lateral mode #3 and the longitudinal mode (mode #5 for with seat and mode #6 for no seat). The addition of the seat and steering column causes a little frequency shift for the 3Dmode (1, 1, 1), which is a combination of longitudinal, lateral and vertical mode. However, the results are counter intuitive because the interior volume of the cavity decreases with the addition of the seat and steering column, which should increase the modal frequencies. The same observation was found in previous publications [4, 8]. In order to further investigate the acoustic modal behavior, a sum block of measured acoustic transfer functions (P/Q) is plotted in Fig. 22.7 for the two cases. The sum block is essentially an averaged response of acoustic transfer functions measured at all microphone locations, which is useful to identify the modes as well as the relative strength of modes. The averaged acoustic transfer function shows that the two cases generally share a similar trend in terms of peaks and valleys in the frequency range of interest except for the mode at 121.2 Hz, which is absent with the addition of the seat and steering
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