14 Study on the Propagation Law of Lamb …
151
Table 14.1 The material
parameters of the 5A06
aluminum-magnesium alloy
Aluminum
designation
Density, ρ
(g/cm 3 )
Young’s
modulus, E
(MPa)
Poisson’s
ratio, μ
5A06
2.64
71,000
0.32
Fig. 14.1 The phase velocity and group velocity dispersion curves of Lamb waves in a 5A06
magnesium-aluminum alloy panel with a thickness of 3 mm: a Phase velocity, b Group velocity
The phase velocity and group velocity dispersion curves of Lamb waves in a 5A06
magnesium-aluminum alloy panel with a thickness of 3 mm are shown in Fig. 14.1.
In non-destructive testing, the frequency of interest is relatively low for Lamb
waves in a panel structure, mainly because the high-frequency Lamb waves are seriously attenuated with increasing distance. At the same time, the high frequency Lamb
wave contains more modalities and the signal is more complicated, which increases
the difficulty of analysis. For the above reasons, it is usually mainly concerned with
the S0 and A0 mode Lamb waves in the lower frequency band.
Compared with the S0 mode, the A0 mode Lamb wave has higher energy.
However, the A0 mode Lamb wave has a slower speed than the S0 mode and reaches
the receiving point after the S0 mode Lamb wave. In the flat structure, the characteristics of the S0 mode Lamb wave and the A0 mode Lamb wave in the time domain
are relatively clear, and they can be distinguished according to the time of reaching
the receiving point. However, in stiffened plats, Lamb waves undergo reflection and
modal transitions when passing through the reinforcement stage. Some A0 modal
Lamb waves convertes into S0 modal Lamb waves, making the characteristics of the
A0 mode Lamb wave are not obvious in the time domain. It is difficult to obtain
the exact arrival time of the A0 mode. In the frequency domain, the A0 mode Lamb
wave overlaps with the S0 mode Lamb wave, and the A0 mode Lamb wave cannot
be extracted from the S0 mode Lamb wave by filtering. The S0 mode Lamb wave is
in a low frequency range and is less affected by the attenuation of the propagation
distance. At the same time, the S0 mode Lamb wave has a fast speed and reaches the
receiving point first. It is not easy to be interfered by other mode Lamb waves in the
time domain.
Based on the influence of the above factors, this paper takes the S0 mode Lamb
wave in the 0–500 kHz band as the research object.
In this paper, the energy ratio is used to measure the effect of the stiffeners on the
Lamb waves of different frequencies. The energy ratio is expressed by the ratio of the
151
Table 14.1 The material
parameters of the 5A06
aluminum-magnesium alloy
Aluminum
designation
Density, ρ
(g/cm 3 )
Young’s
modulus, E
(MPa)
Poisson’s
ratio, μ
5A06
2.64
71,000
0.32
Fig. 14.1 The phase velocity and group velocity dispersion curves of Lamb waves in a 5A06
magnesium-aluminum alloy panel with a thickness of 3 mm: a Phase velocity, b Group velocity
The phase velocity and group velocity dispersion curves of Lamb waves in a 5A06
magnesium-aluminum alloy panel with a thickness of 3 mm are shown in Fig. 14.1.
In non-destructive testing, the frequency of interest is relatively low for Lamb
waves in a panel structure, mainly because the high-frequency Lamb waves are seriously attenuated with increasing distance. At the same time, the high frequency Lamb
wave contains more modalities and the signal is more complicated, which increases
the difficulty of analysis. For the above reasons, it is usually mainly concerned with
the S0 and A0 mode Lamb waves in the lower frequency band.
Compared with the S0 mode, the A0 mode Lamb wave has higher energy.
However, the A0 mode Lamb wave has a slower speed than the S0 mode and reaches
the receiving point after the S0 mode Lamb wave. In the flat structure, the characteristics of the S0 mode Lamb wave and the A0 mode Lamb wave in the time domain
are relatively clear, and they can be distinguished according to the time of reaching
the receiving point. However, in stiffened plats, Lamb waves undergo reflection and
modal transitions when passing through the reinforcement stage. Some A0 modal
Lamb waves convertes into S0 modal Lamb waves, making the characteristics of the
A0 mode Lamb wave are not obvious in the time domain. It is difficult to obtain
the exact arrival time of the A0 mode. In the frequency domain, the A0 mode Lamb
wave overlaps with the S0 mode Lamb wave, and the A0 mode Lamb wave cannot
be extracted from the S0 mode Lamb wave by filtering. The S0 mode Lamb wave is
in a low frequency range and is less affected by the attenuation of the propagation
distance. At the same time, the S0 mode Lamb wave has a fast speed and reaches the
receiving point first. It is not easy to be interfered by other mode Lamb waves in the
time domain.
Based on the influence of the above factors, this paper takes the S0 mode Lamb
wave in the 0–500 kHz band as the research object.
In this paper, the energy ratio is used to measure the effect of the stiffeners on the
Lamb waves of different frequencies. The energy ratio is expressed by the ratio of the