14 Study on the Propagation Law of Lamb …
153
The model uses a grid type of quadrilateral elements, and the grid size is determined according to the wavelength λ to ensure the accuracy of the simulation calculation. Since the maximum frequency f m of the signal under study is 500 kHz and
the shear wave velocity ct in the 5A06 magnesium aluminum alloy is 3198 m/s, the
magnitude of the wavelength is c t /f m with a value of 6.396 mm. Dividing the model
with a signal of 1 wavelength passing at least 10 grids as a standard, the size of
the grid is not larger than 0.6396 mm. The smaller the grid size is, the higher the
calculation accuracy is, and the longer the calculation time is required. If the grid
size is too large, the simulation results will have greater errors. According to the
above analysis, the mesh size is set to 0.5 mm, and the number of seeds required for
each side is calculated based on the length of each side.
At the point (−250, 0), the load is applied in the positive direction of the y-axis,
and the load is applied in the form of a concentrated force.
In non-destructive testing, the frequency of the acoustic emission signal of interest
is below 500 kHz. In order to study the effect of stiffeners on the propagation characteristics of Lamb waves at different frequencies, the simulation signal is a broadband
signal with a frequency of 0–500 kHz. The load is a superimposed sinusoidal signal
with a frequency increasing from 1 to 500 kHz at a frequency of 1 kHz and a load
duration of 20 μs. The load is expressed by (14.4).
F(t) =
⎧
⎪ ⎨
⎪ ⎩
500 kHz
f =1 kHz
sin(2π f t) t ∈ [0.20 μs]
0
t > 20 μs
(14.4)
The time and frequency domain characteristics of the load are shown in Fig. 14.3.
Set the receiving point at point (250, 0) to receive the displacement. Since the
panel is long enough, it is not necessary to consider the influence of the left and
right boundary reflection waves. In many application scenarios, the stiffeners on the
surface of the stiffened panel are usually grid-like periodic distribution. In order to
study the influence of the number of stiffeners on the Lamb wave, the finite element
simulation models with the number of stiffeners of 1–6 were established respectively.
The finite element models of the stiffened panel with 6 stiffeners and the flat panel of
the control group are shown in Fig. 14.4. Based on the above settings, the simulation
is carried out.
Fig. 14.3 a The time domain characteristics. b The frequency domain characteristics
153
The model uses a grid type of quadrilateral elements, and the grid size is determined according to the wavelength λ to ensure the accuracy of the simulation calculation. Since the maximum frequency f m of the signal under study is 500 kHz and
the shear wave velocity ct in the 5A06 magnesium aluminum alloy is 3198 m/s, the
magnitude of the wavelength is c t /f m with a value of 6.396 mm. Dividing the model
with a signal of 1 wavelength passing at least 10 grids as a standard, the size of
the grid is not larger than 0.6396 mm. The smaller the grid size is, the higher the
calculation accuracy is, and the longer the calculation time is required. If the grid
size is too large, the simulation results will have greater errors. According to the
above analysis, the mesh size is set to 0.5 mm, and the number of seeds required for
each side is calculated based on the length of each side.
At the point (−250, 0), the load is applied in the positive direction of the y-axis,
and the load is applied in the form of a concentrated force.
In non-destructive testing, the frequency of the acoustic emission signal of interest
is below 500 kHz. In order to study the effect of stiffeners on the propagation characteristics of Lamb waves at different frequencies, the simulation signal is a broadband
signal with a frequency of 0–500 kHz. The load is a superimposed sinusoidal signal
with a frequency increasing from 1 to 500 kHz at a frequency of 1 kHz and a load
duration of 20 μs. The load is expressed by (14.4).
F(t) =
⎧
⎪ ⎨
⎪ ⎩
500 kHz
f =1 kHz
sin(2π f t) t ∈ [0.20 μs]
0
t > 20 μs
(14.4)
The time and frequency domain characteristics of the load are shown in Fig. 14.3.
Set the receiving point at point (250, 0) to receive the displacement. Since the
panel is long enough, it is not necessary to consider the influence of the left and
right boundary reflection waves. In many application scenarios, the stiffeners on the
surface of the stiffened panel are usually grid-like periodic distribution. In order to
study the influence of the number of stiffeners on the Lamb wave, the finite element
simulation models with the number of stiffeners of 1–6 were established respectively.
The finite element models of the stiffened panel with 6 stiffeners and the flat panel of
the control group are shown in Fig. 14.4. Based on the above settings, the simulation
is carried out.
Fig. 14.3 a The time domain characteristics. b The frequency domain characteristics