Keywords

1 Introduction

An ocean bottom seismometer (OBS) is a geophone put on seabed for three-component data acquisition, and ocean bottom seismometers are widely used for study on the deep crust-mantle structure of the earth [1, 2]. With the development in the fields of OBS apparatus development and deep detection technology in China, China has carried out study on application of OBS in shallow-water continental crust areas, such as Bohai Sea, on the basis of using an OBS for detection of the deep structure of a deep sea, and has conducted seabed detection mainly with an OBS carried by a simple cross-frame-type sinking coupling frame [3]. However, owing to growing marine engineering works and frequent fishing activities in the coastal shallow-water areas, the apparatuses put on seabed in shallow-water areas were often damaged by impact or dragged and displaced by fishing boat carried trawls, in particular, the apparatuses were fished out by fishing boat carried trawls and lost, so that valid seismic measurement data could not be obtained finally [4]. In this paper, study on and design of anti-trawl structure for OBS sinking coupling frame were carried out in the environment for placement of OBS in a shallow sea based on the existing work experience, and an engineering sample was made and used in the sea.

Since an OBS has a given working frequency band, and the natural frequency of the OBS anti-trawl sinking coupling frame and the coupling between OBS and sinking coupling frame and that between sinking coupling frame and seabed surface must be taken into full consideration for the purpose of making the acquired data reliable in acquisition of seismic data of seabed, it is crucial to carry out modal analysis of sinking coupling frame. In this paper, based on the structural and technical features of the OBS, modeling of an anti-trawl sinking coupling frame was carried out using the SolidWorks, and modal analysis of the anti-trawl sinking coupling frame was conducted using the large-scale simulation analysis software ANSYS Workbench. The natural frequencies and mode shape contour diagrams of various modes of the sinking coupling frame were obtained. Based on comparative analysis of the natural frequencies of the sinking coupling frame and the working frequency range of the OBS, the structure of the sinking coupling frame was optimized, so resonance was avoided. This provides a theoretical basis for the rationality of the structural design of the sinking coupling frame.

2 Basic Theory of Modal Analysis

Modes are the natural vibration characteristics of a structural system, and the natural frequencies and natural mode shapes of a structure are the bases for analysis of the dynamic response and other dynamic characteristics of the structure. An anti-trawl sinking coupling frame is a vibration system with N degrees of freedom. According to mechanics theory, the general equation of motion of an object in vibration mechanics is as follows:

$$ {{\varvec{Mx}}} + {{\varvec{Cx}}} + {{\varvec{Kx}}} = {{\varvec{F}}}(t) $$
(1)

where M is the mass matrix, C is the damping matrix, K is the stiffness coefficient matrix, x is the displacement vector, and F is the excitation force vector.

The damping value of the vibration system of the anti-trawl sinking coupling frame structure is very small and it has quite little influence on the self vibration frequency of the system, so the influence of the damping value can be neglected in modal analysis of the anti-trawl sinking coupling frame structure to calculate the natural frequencies and mode shapes. Consequently, the natural frequencies and mode shapes of the structure can be studied by solving for undamped vibration under the condition of no external load, and Eq. (1) is simplified as:

$$ {{\varvec{Mx}}} + {{\varvec{Kx}}} = 0 $$
(2)

It can be known from vibration theory that the analytical solution of free vibration of the system is:

$$ x = A\sin (\omega_{n} t + \phi ) $$
(3)

where A is the principal mode shape, i.e., the mode shape of the system; ωn is the natural frequency of the system; and φ is the phase angle.

When Eq. (3) is substituted into Eq. (2), the following can be obtained:

$$ ({{\varvec{K}}} - \omega_{n}^{2} {{\varvec{M}}})A = 0 $$
(4)

Equation (4) is a multi-degree-of-freedom dynamic characteristic equation, with non-zero solutions existing, it has n eigenvalues, i.e., ω1, ω2, …, ωn, and ωi is the natural frequency of the ith mode of the system [5].

3 Composition of the Anti-trawl Sinking Coupling Frame

The OBS anti-trawl sinking coupling frame designed in this paper was mainly composed of such parts as seabed coupling panel, guardrail, side support bracket, OBS release opening, rope storage box, chassis, and anti-trawl shield, and the OBS was mounted on the chassis.

The OBS anti-trawl sinking coupling frame employed a frustum-shaped streamline design with relatively high strength, which could effectively prevent the sinking coupling frame platform and the carried OBS from being damaged by various fishing boat carried trawls, and flow nets. The design diagrams are shown in Fig. 1 and the real object pictures are shown in Fig. 2.

Fig. 1
2 diagrams of a volcano-shaped structure. 1, The external slope of the structure is marked 8. 2, The dome-like component at the center is 1, a plate at the bottom is 2, a bar cage is 3, slope bars are 4, the upper rim of the cage is 5, a cylindrical component is 6, and the rim at the base is 7.

Diagrams of the OBS anti-trawl sinking coupling frame. 1-OBS, 2-Seabed coupling panel, 3-Guardrail, 4-Side support bracket, 5-OBS release opening, 6-Rope storage box, 7-Chassis, 8-ANTI-trawl shield

Full size image
Fig. 2
2 Photos capture the external and the internal view of the volcano-shaped structure. The structure has a dome-like component at the center which is surrounded by a bar cage that has 2 circular rims on the top and the bottom.

Real object pictures of OBS anti-trawl sinking coupling frame

Full size image

In the design, three-dimensional modeling of an OBS anti-trawl sinking coupling frame was carried out using the ANSYS, and then finite element analysis of the sinking coupling frame was conducted with the modal analysis types in the software ANSYS Workbench [6], as shown in Fig. 3. The material of the sinking coupling frame was austenitic stainless steel of a given model number, and the material properties are shown in Table 1.

Fig. 3
A diagram of the volcano-shaped structure with a dorsolateral view. The body and the inner components appear dark.

Finite element analysis model of the anti-trawl sinking coupling frame

Full size image
Table 1 Material properties
Full size table

4 Analysis of the Anti-trawl Sinking Coupling Frame

To prevent the OBS anti-trawl sinking coupling frame from resonance under the undersea conditions, the natural frequencies and mode shapes of the sinking coupling frame need to be calculated. In this paper, modal analysis of the sinking coupling frame was carried out using the constraint modal analysis method under the condition that the sinking coupling frame was only subjected to gravity without any external force applied. The bottom of the sinking coupling frame, which came into contact with the seabed surface, was fixed with full constraints [7], and finite element gridding of the sinking coupling frame was carried out using the free gridding method. The density of grids was increased according to the mean value, and 182, 481 grids in total were generated, with the number of nodes of 366, 244. Figure 4 shows the schematic diagram of gridding.

Fig. 4
A diagram of the volcano-like structure with a dorsolateral view. The body appears dark with shaded spots all over it. The internal grids have markings all over them.

Schematic diagram of gridding

Full size image

After fixation constraints were applied to the bottom of the anti-trawl sinking coupling frame, the natural frequencies and natural mode shapes of the OBS anti-trawl sinking coupling frame were calculated through simulation. The mode shapes of the first six modes are shown in Fig. 5, and the natural frequencies of various modes of the sinking coupling frame and corresponding maximum deformation values are shown in Table 2.

Fig. 5
6 contour diagrams of the mode shapes of the volcano-like structure with an aerial view. The body and the grid have a shade that has a 0 value. The body has shaded spots based on the color gradient scale that varies for the first, second, third, fourth, fifth, and sixth modes.

Mode shapes of the first six modes

Full size image
Table 2 Natural frequencies of various modes of the sinking coupling frame
Full size table

The mode shapes of low-order modes determined the dynamic characteristics of a structure, and had higher influence on the dynamics of the structure than high-order modes [8]. The working frequency of the OBS ranged from 0.0083 to 100 Hz. In theory, the designed resonance frequency of the anti-trawl sinking coupling frame should evade 100 Hz. Moreover, there might be mutual influences between modes. According to general experience, a frequency range 1.5–2 times the frequency of vibration source needed to be considered, so all resonance frequencies below 200 Hz should be avoided. It can be known from the analysis that the deformation of the sinking coupling frame was mainly shield deformation. The natural frequency of the first mode of the shield was 237.09 Hz, and it effectively evaded the working frequency band of the OBS, avoiding the resonance phenomenon.

5 Analysis of the Seismic Response Spectrum

Spectral analysis is an extension of modal analysis, and the spectra represent the response of a single-degree-of-freedom to time-related load. Spectral analysis can make the modal analysis results associated with a spectral curve, to calculate the displacement and stress of the structure from the perspective of frequency domain, thus to determine the dynamic response of the structure to a random load [9].

In this paper, analysis of mechanical strength of the anti-trawl sinking coupling frame was carried out using the single-point response spectrum analysis method, with fixation constraints applied to the bottom of the anti-trawl sinking coupling frame. The equivalent stress contour diagram and displacement contour diagram of the sinking coupling frame was obtained through simulation analysis, as shown in Figs. 6 and 7.

Fig. 6
A contour diagram of the volcano-like structure with an aerial view. The body and the grid have a shade that ranges between 7.2468 e minus 10 and 0.40771. The slope has shaded spots that mostly range from 0.40771 to 2.4463.

Equivalent stress contour diagram of the anti-trawl sinking coupling frame

Full size image
Fig. 7
A contour diagram of the volcano-like structure with an aerial view. The body and the grid have a shade that ranges between 0 and 0.0024187. The slope has shaded spots that mostly range from 0.0048373 to 0.021768 from the periphery to the core of the spots.

Displacement contour diagram of the anti-trawl sinking coupling frame

Full size image

As can be discerned from Fig. 6, the maximum stress of the anti-trawl sinking coupling frame is 3.6694 MPa, occurring in the shield of sinking coupling frame, and it is less than the yield limit of austenitic stainless steel, so the strength of the sinking coupling frame meets the requirement. It can be discerned from Fig. 7 that the maximum deformation value of the sinking coupling frame is 0.021768 mm, which is very small. It can be known from summarizing the above analyses that this sinking coupling frame structure meets the requirements.

6 Conclusions

Through analyses of an OBS anti-trawl sinking coupling frame with the above methods, the following conclusions could be made:

  1. (1)

    The vibration frequencies of an OBS anti-trawl sinking coupling frame can be determined. Comparing the natural frequencies of the sinking coupling frame structure obtained from analysis with finite element analysis software with the working frequency range of the OBS can achieve avoidance of resonance phenomenon. This method demonstrates that it is feasible to avoid resonance through finite element analysis.

  2. (2)

    Through finite element modal analysis, the natural frequencies of various modes of the OBS anti-trawl sinking coupling frame effectively evaded the working frequency band of the OBS and would not influence the results recorded by the OBS, and resonance phenomenon was avoided. This demonstrates the rationality of the structural design of the sinking coupling frame.

  3. (3)

    According to the spectral analysis, the shield of sinking coupling frame underwent relatively large stress and had relatively great displacement, but the overall stiffness of the sinking coupling frame was high and the structural design met the requirements.