This paper is concerned with the sinking of the Korean naval warship (ROKS Cheonan) and the reported spectra of the seismic signals recorded at the time of the incident. The spectra of seismic signals show prominently amplitude peaks at around 8.5 Hz and its harmonics. These frequencies were explained with the vibrations of a water column due to an underwater explosion. This explanation is highly doubtful and concerns about its validity have already been raised in the scientific community. In this work an alternative explanation is presented: it is shown that the recorded seismic spectra are consistent with the natural frequencies of vibrations of a large submarine with a length of around 113 m. This finding raises the possibility that the ROKS Cheonan sunk because of the collision with a large submarine rather than the explosion of a torpedo or an underwater mine.
Several years have passed since the incident of the Korean naval warship (ROKS Cheonan) sinking that occurred on the 26th of March 2010 [
(a) ROKS warship; (b) top view. Sketch of the part damaged during the incident.
This work was motivated from the report of [
This statement in our opinion is a speculation and no proof or simulations to support it were shown in [
We think that it is worthwhile to search an alternative theory to explain more properly the spectra including amplitudes of the seismic signals. For instance, it will be shown in this work that a possible explanation for the sinking of the ROKS Cheonan warship is a collision with a large submarine. The reason for this explanation relies on the fact the frequencies observed in the spectra of the seismic data are consistent with the natural frequencies of vibrations of a large submarine, as it will be shown later in the paper. The collision of the ship with the submarine would generate a large force transmitted to the submarine hull with the consequent structure born sound radiated in the sea-water. The sound waves then transmit into the earth crust as seismic waves and can be recorded at seismic detecting stations. The purpose of this paper is to explore this possibility to gain insight into the reality of the cause of the Cheonan sinking. For this aim both a simplified and more accurate model of a submarine hull will be presented in the following sections. A simplified model will be used first to find the main dimension of the submarine hull; a more realistic model will be then used to properly match the seismic signature.
A model of a submarine is presented according to the approach of [
(a) Schematic diagram of the more realistic model of a submarine for the free-free cylindrical shell with bulkheads, stiffeners, and closed by plates following conical end caps. (b) Cylindrical coordinate system (
At first, let us consider a cylindrical shell of length
If
Comparison of the natural frequency of the simplified model structure (
( |
Simplified model | Realistic model |
---|---|---|
Natural frequency (Hz) ( |
Resonant frequency (Hz) | |
(0, 1) | 8.5 (0.999, 0.022) | 8.6 |
(0, 2) | 17.1 (0.999, 0.046) | 17.4 |
(0, 3) | 25.5 (0.997, 0.046) | 25.7 |
(0, 4) | 34.0 (0.994, 0.105) | 35.5 |
|
||
( | ||
(1, 1) | 0.9 (0.104, 0.705, 0.702) | 1.4 |
(1, 2) | 3.3 (0.175, 0.701, 0.691) | 3.5 |
(1, 3) | 6.6 (0.210, 0.698, 0.684) | 6.3 |
(1, 4) | 10.4 (0.219, 0.696, 0.684) | 9.3 |
(1, 5) | 14.3 (0.212, 0.693, 0.689) | 12.4 |
(1, 6) | 18.2 (0.197, 0.686, 0.700) | 14.7 |
For the
Figures
Frequency response function for an axial force applied to the submarine end.
Frequency response function for a radial force applied to the submarine end.
The striking feature in Figure
It has to be mentioned that the purpose of this calculation is to show the FRF of the submarine model and its natural frequencies, and a possible qualitative correlation with the seismic data recorded. In reality the exact impact point on the hull, the actual force transmitted to the submarine, and its frequency content would surely affect the quantitative results but an exact reconstruction of the impact it is surely a huge and uncertain task and is out of the scopes of this work.
The sound pressure radiated at far field was also calculated using the model in [
Far field wave displacement for axial force acting on the submarine end.
Figure 7 of [
The amplitude data of the peaks in the frequency spectrum reported in Figure
|
|
|
|
|
Cal.* |
---|---|---|---|---|---|
8.5 | 10−8.22 | 6.0 | 1.0 | 1.0+ | 1.0 |
17.7 | 10−8.88 | 1.3 | 0.22 | 0.45 | 0.23 |
26.0 | 10−9.40 | 0.4 | 0.07 | 0.20 | 0.04 |
34.6 | 10−10.17 | 0.07 | 0.01 | 0.05 | 0.016 |
The amplitude data of the peaks in the normalized frequency spectra for
|
|
EW | NS | Av.* |
---|---|---|---|---|
8.5 | 1.0 | 1.0 | 1.0 | 1.0 |
17.0 | 0.30 | 0.38 | 0.22 | 0.30 |
25.5 | 0.13 | 0.17 | 0.10 | 0.13 |
34.0 | 0.03 | 0.03 | 0.02 | 0.03 |
In [
In summary the main peaks at 8.5 Hz and its multiples in the reported spectra of the seismic signals are reasonably consistent with the natural frequencies of the submarine with a length of around 113 m. This result suggests a possibility of the collision between the Cheonan warship and the submarine. Then one might wonder about the damage that the submarine would have following a collision. We believe that the submarine would be negligibly damaged by the collision since the thickness of the hull of a large submarine is supposed to be more than 6 cm with and made of high strength steels, while the hull thickness of the ROKS Cheonan is known to be about 1.2 cm with steels and aluminum alloys in the upper parts. Besides we have found that it is no difficult with this collision theory discussed in this paper to illustrate damage aspects including deformations on the recovered bow and the stern of the split Cheonan warship from the sinking.
This study shows that the characteristic frequencies at spectral peaks of the seismic signals recorded at the time of the Cheonan incident are consistent with the natural frequencies of vibrations of a large submarine with a length of around 113 m. The matching is particularly good with the axisymmetric (
Several doubts have been raised about the JIG’s report and they are explained in what follows. The first issue of the controversy over the JIG’s report [ the split ROKS Cheonan recovered in April of 2010; the remnants of a torpedo retrieved near the incident site on 15 May 2010; the explosion products from the small-scale explosion experiment using a highly aluminized explosive source of 15 g in a tank filled with 4.5 tons of seawater.
The composition analysis was performed with data obtained from SEM (scanning electron microscopy), EDS (energy dispersive spectrometer), and XRD (X-ray diffraction) for all three cases. The analysis was based on their knowledge or assumption:
The second issue about JIG’s report is whether the torpedo remnants were genuine or not. Inside the rear section of the torpedo remnants, JIG found Korean handwrite marking “1bun (No. 1 in English in blue ink)”, similar to the marking of a North Korean test torpedo obtained in 2003, as seen in
This result means that at least the C sample was quite different from the A and B samples, and in turn JIG’s conclusion above is very questionable, as Lee has concluded. Lee and Yang then reported their own experimental results in another study [
Cyranoski [ An expert investigator was placed on the JIG by the opposition party—Shin Sang-chul, a former officer in the South Korean navy who had also worked at a shipbuilding company—suggested, before the report was even released, that an accidental collision with a US warship, and not North Korea, was to blame. The United States and South Korea had been carrying out military exercises in the area at the time. Now he is insisting on the collision with a submarine with a length of around 60 m, not by a US warship. The report’s claim that a torpedo-induced water column sank the
Lee and Suh in [
“If the bottom of the ship was hit by a bubble, it should show a spherical concave deformation resembling the shape of a bubble, as the JIG’s own simulation suggests in the Appendix of the report, but it does not. The bottom of the front part of the ship is pushed up in an angular shape, as the yellow line shows in
Kim et al. in “Foreign Policy In Focus” [
The Flügge equations of motion for the vibrations of a ring stiffened cylindrical shell are given by Caresta and Kessissoglou [
Suppose that the shell is axially excited at one end by a point force of unity amplitude located at (
The optimized path of the signals arriving at the BAR station from the submarine is drawn in Figure
The authors declare that there is no conflict of interests regarding the publication of this paper.