When the submarine is sailing at full speed, the power cabin has an abnormally high temperature. However, in the previous research on the vibration reduction design of the foundation, the influence of high temperature on the vibration characteristics of the foundation is not taken into account. In this paper, a new composite foundation with entangled metallic wire material (EMWM) is presented to reduce the vibration of the foundation. The energy transfer path of the foundation was obtained by the power flow method, and then the layout of EMWM was determined. The optimization of the constraining layer was carried out by modal analysis. The damping performance of the composite foundation with EMWM was validated by the thermal-vibration joint test. The results show that, at room temperature, the composite foundation has remarkable vibration reduction efficiency in the middle and high-frequency bands. The maximum insertion loss can reach 15.37 dB. The insertion loss varies with the location of the excitation point. As the temperature rises to 300°C, the insertion loss in the low-frequency band was improved, and the insertion loss is not influenced by the excitation position.
In modern warfare, the acoustic stealth performance of submarines directly affects their survival and attack. The prime sources of underwater noise for submarines are fluid noise, machinery noise, and structural borne noise [
The foundation is a key link of the vibration transmission path. The vibration characteristic of the foundation is related to the acoustic stealth performance of submarines. The foundation is usually designed as an elastic support structure with damping function. However, some equipment and structures connected to the power machine often have more stringent alignment requirements, such as the installation of tail shaft and gear box. In this case, the foundation is designed to be rigid. Thus, flexible vibration isolation technology cannot be used to reduce the vibration of rigid foundation. To solve this problem, there are three methods to reduce the vibration of rigid foundation: adding blocking masses, using composite foundation, and laying viscoelastic damping material [
The foundation is composed of several plates, and the blocking masses are often added to the plates for reflecting or suppressing vibration wave at specific wavelengths. Shi et al. [
Composite foundation made of new materials, such as carbon fiber-reinforced composite materials, has better damping performance. Zhang et al. [
The core material and the panel with strong energy absorbing performance can form a sandwich structure, which has broad application prospects in ship vibration reduction. Compared with free damping, the constrained damping produces a larger shear strain under harmonic excitation, resulting in more energy dissipation. The current research mostly focuses on the dynamic performance of the sandwich panel. Merideno et al. [
The vibration reduction design of foundation under high temperature is still a difficult technical problem. Traditional polymer materials such as rubber will accelerate aging with the rise of temperature. When the temperature is too high, the damping material may even crack and carbonize, which will greatly reduce its service life. A variety of new damping materials have emerged, and the most representative of which is entangled metallic wire material (EMWM) [
To reduce the vibration of the foundation under high temperature, a composite foundation with entangled metallic wire material is proposed. A power flow calculation is performed to determine the position for laying EMWM. A modal analysis of the foundation is conducted for optimizing the constraining layer. Finally, a thermal-vibration joint test for foundation is conducted to validate the proposed method.
Entangle metallic wire material is a metallic damping material. In this paper, the EMWM layer is made of 304 (06Cr19Ni10) stainless steel wires. The preparation of the EMWM is referring to [
Mold and rough porous base material of EMWM. (a) Schematic diagram of the pressing mold. (b) Rough porous base material of EMWM.
The EMWM specimens are shown in Figure
EMWM specimens.
Formation parameters.
EMWM type | S | M | L |
---|---|---|---|
Dimension (mm) | 84 × 74 × 4 | 168.5 × 74 × 4 | 249 × 74 × 4 |
Density ( |
2.595 | 2.596 | 2.584 |
Forming pressure (kN) | 1260 | 1890 | 2394 |
As shown in Figure
Two-dimensional schematic diagram of the EMWM insertion damping structure.
When the baseplate is excited, the baseplate will produces a displacement response, and the constraining layer will also produces a displacement response. The deviation in the displacement between baseplate and constraining layer will cause the EMWM layer to produce tension-compression deformation. When the entangled metallic wire material is deformed in micron scale, the internal metal wire will slip and lead to energy dissipation [
A simplified foundation is used as the research subject, and its dimensions are shown in Figure
Structural parameters of steel foundation.
Thickness of each plate of the foundation.
Name | Thickness (mm) |
---|---|
Face plate | 20 |
Web plate | 12 |
Bracket | 9 |
Connection plate | 8 |
The foundation and the fixed plate are made of 45 steel (C45E4). The material properties of 45 steel are as follows: density is 7890
Thermophysical properties of 45 steel.
Temperature (°C) | 20 | 300 |
---|---|---|
|
210 | 196 |
|
11.59 | 13.09 |
The lightweight of ships or submarines is an important technical specification, which should be considered in the design of composite foundation. Power flow can reflect the relationship between the magnitude and phase of force and velocity vector. It means that it can describe the vibration more comprehensively. Therefore, the power flow is selected as an evaluation index to reflect structural vibration [
The foundation is mainly composed of several flat-plate structures. When a flat-plate structure is excited by a single-frequency steady-state force, in consideration of the thickness of the plate, the power flow per unit width
Internal force and displacement of the flat unit.
In this paper, the laying position of EMWM is determined by the power flow distribution of the foundation.
The first-order natural frequency of the foundation is larger than that of the fixed plate. To avoid the influence of the fixed plate, the vibration of the foundation is analyzed separately. The boundary condition of the foundation is set as clamped. The excitation points are located at the center and the corner of the face plate, respectively. The finite element model, excitation points, and boundary conditions are shown in Figure
The finite element model, excitation points, and boundary conditions.
The modal response and power flow of the foundation are solved by direct method with the commercial software “ABAQUS.” The sweep frequency is set to 10 Hz–500 Hz. The sweep rate is 1 oct/min. A unit excitation is applied at points A and B, respectively. The thermal expansion force will replace the excitation force at high temperature, and thus the power flow of the foundation is solved only at room temperature (20°C). Taking the second-order natural frequency as an example, the results of the calculation are shown in cloud and vector diagram, as shown in Figure
Power flow cloud and vector diagram of foundation at room temperature. The incentive is located at (a) point A and (b) point B (unit: watt).
As shown in Figure
Arrangement scheme of the composite foundation.
As shown in Figure
SEM image of the EMWM (100x enlargement).
The energy dissipation of the EMWM insertion damping structure is determined by the deformation of the EMWM layer. The EMWM was constrained by the foundation and constraining layers. The displacement deviation between the foundations and constraining layers will cause the EMWM layer to produce tension-compression deformation. The greater the displacement deviation, the more energy is dissipated by the EMWM. Therefore, to maximize the energy dissipation, the arrangement of bolts and the thickness of the constraining layer should be optimized to maximize the displacement deviation.
Considering the location and the thickness of the EMWM layer, the thickness of the constraining layer is limited to 2∼7 mm, and two bolt fixing methods are compared, as shown in Table
Installation methods of bolts.
Installation method | |
---|---|
BA1 | Four bolts, fixed at four corners |
BA2 | Two bolts, diagonally fixed at positions 2 and 4 |
FEM model of each laying position.
The modal analysis of the foundation is conducted by the use of ABAQUS. The optimization method is as follows:
The boundary condition is set to be fixed at the bottom of the supports, and the temperature is 300°C. The displacement deviation between each position of the foundation and the corresponding constraining layer at the first three natural frequencies is obtained by modal calculation, as shown in Figures
Displacement deviation between foundation and constraining layers in the position of the face plate. (a) Position
Displacement deviation between foundation and constraining layers in the position of the bracket. (a) Position
Displacement deviation between foundation and restraint layers in the position of the web plate. (a) Position
Displacement deviation between foundation and restraint layers in the position of the connection plate. (a) Position
It can be seen from Figure
In Figure
The first two modes of the foundation are forward-backward bending mode and up-down translational mode, respectively. Therefore, for the area of the foundation other than the bracket, when the thickness of the constraining layer increases, the bending mode should make the constraining layer form a larger displacement deviation between constraining layer and foundation due to the difference between the inside and outside. But, as the thickness of the constraining layer increases, the stiffness of the part, where the constraining layer is located, will increase at the same time. Thus, as shown in Figures
As can be seen from Figures
The curves of
The curves of
In the first and third modes, the curves of the displacement deviation between constraining layer and foundation at two positions of the web plate show a downward trend. However, they show an upward trend in the second mode, the corresponding value of the curve is smaller than that in the other modes. Thus, the thinnest constraining layer of the web plate is selected.
The curves of the displacement deviation between constraining layer and foundation at two positions of the connection plate show a downward trend in the first three modes. Therefore, the thickest constraining layer is selected.
In summary, the final thickness of the constraining layers is shown in Table
Thickness of the constraining layer (unit: mm).
Position | Face plate | Bracket | Web plate | Connection plate | ||||
---|---|---|---|---|---|---|---|---|
|
|
|
|
|
|
|
| |
Upper constraining layer | 2 | 2 | 7 | 2 | 2 | 2 | 2 | 2 |
Lower constraining layer | 2 | 2 | 7 | 2 | 2 | 2 | 2 | 2 |
As can be seen from Figures
In this section, the modal simulation results will be validated by experimental modal analysis. Young’s modulus of 45 steel will change under different temperatures. However, the difference between the modal analysis results at high temperature and those at room temperature is small. Thus, the modal validation of the steel foundation is carried out only at room temperature.
As shown in Figure
Test modal device.
The test results and simulation results are shown in Table
Natural frequencies and vibration modes of test and simulation.
Number | Vibration mode | Frequency (Hz) | Error (%) | |
---|---|---|---|---|
Simulation | Test | |||
1 | Bending | 55.8 | 56.3 | 0.90 |
2 | Translation | 90.6 | 91.1 | 0.50 |
3 | Bending | 111.2 | 97 | 14.60 |
4 | Bending | 115.6 | 137.6 | 16.00 |
5 | Partial bending | 337.8 | 318.5 | 6 |
6 | Partial bending | 350.1 | 355.1 | 1.40 |
7 | Partial bending | 360.6 | 360.6 | 0 |
8 | Partial bending | 367.1 | 364.8 | 0.60 |
9 | Partial bending | 417.3 | 401.4 | 4.00 |
10 | Partial bending | 443.3 | 442.4 | 0.20 |
In order to complete the experiment at a high temperature, a thermal-vibration joint test system is developed by our team [
Block diagram of the thermal-vibration joint test system.
A temperature rise test was performed to evaluate the effect of temperature control. The target temperature was set as 100°C, 200°C, and 300°C, respectively. The temperature was kept for one hour at the target temperature to ensure that the foundation can be uniformly heated. Figure
Preset and control temperature on the web plate.
The thermal-vibration joint test system for the foundation is shown in Figure
The thermal-vibration joint test system for foundation. (a) Test arrangement. (b) Composite foundation and temperature measuring point. (c) Temperature sensor.
The arrangement of excitation point and measurement points.
The electromagnetic exciter sends sinusoidal sweep force to continuously excite the foundation. The parameters of the excitation signal are given in Table
The parameters of the excitation signal.
Parameters | Numerical value |
---|---|
Amplitude | 80 N |
Waveform | Sine |
Sweep mode | Logarithmic |
Sweep range | 10∼1000 Hz |
The thermal-vibration joint test results of rigid foundation and composite foundation under room temperature and high temperature are shown in Figure
Acceleration admittance curve of steel foundation and composite foundation under different excitation points and temperatures. (a) 20°C, excitation point A; (b) 20°C, excitation point B; (c) 300°C, excitation point A; (d) 300°C, excitation point B.
Under room temperature, the peak value of
Under high temperature,
As is shown in Figure
In this paper, the power flow was used as the evaluation index, and the energy transfer path of the foundation under single-point excitation was obtained. To reduce the vibration of the foundation, an EMWM composite foundation was designed. The reliability of the simulation and the damping performance of the composite foundation were validated by the modal validation and the thermal-vibration joint tests. The main conclusions, which can be drawn from the conducted simulations and tests, are as follows: The thickness of the horizontal constraining layer, such as the face plate and the connection plate, is negatively correlated with the displacement deviation between constraining layer and foundation. However, the relationship between the thickness of the constraining layer and the displacement deviation between constraining layer and foundation at the vertical plates, such as the brackets and the web plate, are complicated, and the change trend is changed according to the local stiffness and the various modes. When the ambient temperature is 20°C or 300°C, the composite foundation can effectively suppress the vibration in the analysis frequency band. The maximum vibration attenuation value can reach 15.37 dB. The attenuation value of the low-frequency band is slightly improved at a higher temperature than at room temperature. In addition, the insertion loss at room temperature changes slightly with the change of the excitation point, and the insertion loss does not change at high temperatures. The insertion damping structure with the entangled metallic wire material is presented. The damping performance of this structure is stable and effective at different temperatures.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare no conflicts of interest.
This study was supported by the National Natural Science Foundation of China (grant no. 51805086) and the Natural Science Foundation of Fujian Province, China (grant no. 2018J01763).