Table 2.
Natural frequencies ωn and damping ratios ξn of the first 19 modes of the MDF plate, identified using a frequency-domain method from an FRF, and the time-domain method from free vibration responses, either from acceleration (acc) or radiated sound (mic). The relative errors, expressed as percentages, are calculated with respect to the values identified from the FRF, which are taken as reference values.
| n | ωn/2π (Hz) |
ξn (%) |
||||
|---|---|---|---|---|---|---|
| FRF | acc | mic | FRF | acc | mic | |
| 1 | 219.4 | 219.4 (0.00%) | 219.3 (−0.02%) | 1.03 | 1.02 (−0.6%) | 1.02 (−1.3%) |
| 2 | 322.6 | 322.8 (0.09%) | 321.8 (−0.23%) | 1.04 | 1.04 (0.3%) | 1.29 (23.7%) |
| 3 | 392.6 | 392.5 (−0.03%) | 392.5 (−0.01%) | 1.08 | 1.10 (1.1%) | 1.08 (−0.5%) |
| 4 | 547.1 | 547.2 (0.00%) | 547.0 (−0.02%) | 1.00 | 1.00 (−0.2%) | 0.99 (−1.8%) |
| 5 | 572.0 | 571.9 (−0.03%) | 572.2 (0.03%) | 1.00 | 0.99 (−1.2%) | 1.04 (4.1%) |
| 6 | 918.1 | 918.3 (0.03%) | 918.2 (0.02%) | 1.03 | 1.02 (−1.5%) | 1.02 (−1.5%) |
| 7 | 1000.7 | 1001.6 (0.09%) | 1001.0 (0.03%) | 1.37 | 1.27 (−7.2%) | 1.53 (12.1%) |
| 8 | 1023.4 | 1023.1 (−0.03%) | 1023.0 (−0.03%) | 0.92 | 1.06 (14.9%) | 1.24 (34.6%) |
| 9 | 1090.7 | 1090.5 (−0.02%) | 1088.3 (−0.22%) | 0.95 | 1.01 (5.9%) | 0.96 (0.4%) |
| 10 | 1211.1 | 1210.7 (−0.03%) | 1210.4 (−0.06%) | 1.05 | 1.02 (−2.9%) | 1.04 (−1.5%) |
| 11 | 1599.2 | 1600.6 (0.08%) | 1597.1 (−0.13%) | 1.18 | 1.14 (−3.8%) | 1.20 (1.7%) |
| 12 | 1643.8 | 1644.5 (0.04%) | 1647.6 (0.24%) | 1.07 | 1.09 (1.5%) | 0.92 (−14.5%) |
| 13 | 1743.5 | 1744.6 (0.06%) | – | 1.00 | 1.02 (2.2%) | – |
| 14 | 1911.5 | 1912.3 (0.04%) | – | 1.02 | 1.04 (2.3%) | – |
| 15 | 1946.6 | 1971.6 (1.28%) | – | 1.89 | 2.40 (27.1%) | – |
| 16 | 2090.5 | 2084.4 (−0.29%) | – | 1.23 | 1.26(2.7%) | – |
| 17 | 2282.7 | 2280.9 (−0.08%) | – | 1.16 | 1.18 (1.1%) | – |
| 18 | 2382.8 | 2383.9 (0.05%) | – | 1.05 | 0.85 (−18.8%) | – |
| 19 | 2536.2 | 2533.9 (−0.09%) | – | 1.05 | 1.31 (25.1%) | – |
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