Master Thesis - OUFTI-1

• Young's modulus: E = 205 GP a
• Poisson ratio: ν = 0.3
• Density: ρ = 7850 kg/m 3
Consider also that the plate has a constant thickness of 1.6 mm (which is the given
thickness of OUFTI-1 PCBs). This plate was meshed once with volume elements and
once with shell elements. Then, the two sets of results are correlated. The most popular
correlation techniques make use of natural frequencies ω and mode shapes φ. And, the
most popular indicators of the correlation between two sets of data are:
• The frequency deviation, that can be calculated using Equation 4.2.3.
This indicator is generally expressed in %.
∆f (ω 1 , ω 2 ) = |ω 1 − ω 2 |
ω 1
(4.2.3)
• The Modal Assurance Criterion (MAC), that can be calculated using Equation 4.2.4.
MAC (φ 1 , φ 2 ) =
(
φ
T
1 φ 2
) 2
(φ T 1 φ 1 ) (φ T 2 φ 2 )
(4.2.4)
MAC values oscillate between 0 and 1, a unitary value meaning perfect correlation.
The results obtained by using these two indicators in our particular case, are presented
in Table 4.1 and in Figure 4.5.
Natural frequencies obtained Natural frequencies obtained Frequency
using volume elements (Hz) using shell elements (Hz) deviations (%)
1 528.2 527.8 0.08
2 771 770.2 0.1
3 954.8 953.8 0.1
4 1364.1 1361.9 0.16
5 1364.1 1361.9 0.16
Table 4.1: Frequency deviations between the two models
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