To reduce the vibration of the plate-like structure under different boundary conditions, an all-metal damping composite structure was proposed, and its damping layer was entangled metallic wire material (EMWM). A series of quasi-static compression tests were carried out to investigate the damping property of the EMWM layer. A modal test system was set up to evaluate whether the EMWM could dissipate vibration energy. The evaluation results showed that the displacement deviation between the baseplate and constraining plate of the structure was large enough and the EMWM could dissipate vibration energy in the form of friction. The modal characteristics of the composite structure with different core thicknesses under different boundary conditions were researched in this paper by experimental modal tests. The outcomes showed that the damping ratio of the structure would be significantly improved by adding EMWM and constraining plate. The larger the thickness of the core thickness is, the larger the damping ratio and vibration reduction performance of the composite structure are. This paper provides a new technical way for the damping design of high temperature plate structure.
Vibration and noise are ubiquitous in the fields of aviation, automobiles, ships, and buildings. These vibrations and noise will accelerate the fatigue damage of the structure, shorten the service life of the equipment, affect the comfort of the working and living environment, and even harm the health of the human body. Research on reducing vibration and noise by strengthening structural stiffness or improving structural energy dissipation performance has been done by many researchers.
Viscoelastic materials are widely used to mitigate the vibration in the form of constrained layer dampers (CLD) or free layer dampers (FLD). It has been proved that CLD is more effective than FLD for a given added weight [
Entangled metallic wire material (EMWM) is a porous material with high damping properties. EMWM is made of various entangled metallic wire helixes. The damping mechanism of the EMWM is that when the EMWM is excited by external vibration, the internal wire helixes will slide, fractionate, and extrude, and then the vibration energy will be dissipated and converted into frictional heat energy. The special manufacturing process makes the EMWM have better special mechanical properties than other porous materials, such as high damping, high elasticity, environmental adaptability (high- and low-temperature resistant, antiaging, and nonvolatile), and high sound absorption coefficient. Therefore, EMWM has been extensively investigated and applied [
Plate structure is a common structural shape. The sandwich structure is a kind of plate structure that has been widely studied for its special physical and mechanical properties (damping characteristic, piezoelectric characteristic) [
Sketch of sandwich plate.
The mechanical and damping properties of the EMWM are affected by many factors, such as geometry and density. In previous researches, the EMWM are often processed into cylinders, squares, and so forth to reduce the vibration of the equipment. For vibration reduction of plate-like structure, the EMWM should be processed into a plate and bonded/mounted with the baseplate.
There have been many research results on the simulation, calculation, and experimental analysis of sandwich structure [
Figure
Schematic diagram and physical picture of an equipment base. (a) Schematic diagram. (b) Physical picture.
The EMWM is made of 304 (06Cr19Ni10) stainless steel wires. The manufacture of the EMWM is referring to [
Parameters of the EMWM specimens.
Density (kg/m3) | Length (mm) | Width (mm) | Thickness (mm) | Weight (kg) | Molding pressure (kN) | Batch |
---|---|---|---|---|---|---|
2000 | 150 | 150 | 4 | 0.18 | 132.8 | 1 |
6 | 0.27 | 150.6 | 2 | |||
8 | 0.36 | 156.3 | 3 |
Figure
EMWM specimen. (a) EMWM layer. (b) SEM image of the EMWM (100 × enlargement).
The experimental model proposed in this paper is shown in Figure
Composite structure with EMWM layer.
When the EMWM is deformed in the micron scale, the internal wire helixes of EMWM will slip and lead to energy dissipation [
The damping mechanism of the composite structure with EMWM layer is as follows: when the baseplate is subjected to external excitation, the displacement response of the baseplate and the constraining plate will be generated, respectively, and the deviation of displacement response between the baseplate and the constraining plate will change the deformation of EMWM; then the vibration energy will be dissipated by friction.
The second purpose of this paper is focused on the effect of the boundary condition on the dynamic properties of the composite structure. Therefore, different boundary conditions are applied to the same composite structure, as shown in Figure
Dimensions of the baseplate under different boundary conditions. (a) Two ends clamped (C-C-F-F), (b) three ends clamped (C-C-C-F), and (c) four ends clamped (C-C-C-C).
The composite structure with EMWM layer is shown in Figure
Image of the composite structure with EMWM layer.
In this research, loss factor
Figure
Sketch of the hysteresis loop for EMWM. (a) Energy consumption in one test cycle; (b) maximum deformation energy stored in one test cycle.
The quasi-static compression test for each EMWM specimen was conducted by using a computerized electronic universal testing equipment (WDW-T200). WDW-T200 was manufactured by Jinan Tianchen Testing Machine Manufacturing Co., Ltd., China. WDW-T200 is used in displacement control mode with a constant speed (1 mm/min). To control the test variables, the maximum loading force was set as 35 KN.
The loss factor of each EMWM specimen is shown in Table
Loss factor of EMWM specimens with their standard deviations.
Batch | Thickness (mm) | Mean value | Standard deviation |
---|---|---|---|
1 | 4 | 0.1007 | 0.001 |
2 | 6 | 0.13 | 0.0012 |
3 | 8 | 0.1375 | 0.0014 |
As shown in Figure
Schematic of the modal test system.
The experimental modal test system was mainly composed of a signal source and data acquisition system, a power amplifier, an electromagnetic vibration exciter, and composite structure. For the first test purpose ①, a pair of eddy current displacement sensors were used to measure the displacement response of the baseplate and the constraining plate at the 12 measure points, respectively (Figure
Displacement deviation test system.
The test principle is as follows: (a) the operator installs the composite structure into the test system according to the target boundary condition; (b) the operator sets the experimental parameters on the host computer; (c) the output channels of signal source and data acquisition system generate the corresponding excitation signal; (d) the power amplifier amplifies the signal and then transmits the amplified signal to the electromagnetic vibration exciter; (e) the composite structure received dynamical excitation from the electromagnetic vibration exciter; (f) the signal source and data acquisition system acquires the displacement signals (or acceleration signals) and force signals and sends them to the host computer for postprocessing and storage.
Technical specifications of the main equipment for the test system are as follows: Signal generation and acquisition system: the signal source and data acquisition system (uT8916FRS-DY) was developed by uTekl (Wuhan, China). uT8916FRS-DY has two output channels for generating a sinusoidal sweeping signal and has sixteen input channels for collecting force/displacement/acceleration signals. Electromagnetic vibration exciter: an electromagnetic vibration exciter JZQ-50 is provided with ECON power amplifier (Hangzhou, China). The maximum exciting force was 500 N and the maximum output power was 800 watts. Force measurement: a YD-303 piezoelectric type quartz force sensor (Yangzhou, China). Its resonant frequency was more than 60 KHz and it had a charge sensitivity of 3.08 pC/N. Displacement measurement: two KD9002 eddy current displacement sensors (Yangzhou, China). The parameters of the KD9002 are as follows: the sensitivity was 8 mv/ Acceleration measurement: twelve 1A102 E piezoelectric type accelerometers (Jingjiang, China). The parameters of the accelerometer are as follows: the sensitivity was 10.36 mV/g, and the measuring range was ±500 g.
The parameters of the excitation signal are given in Table
Parameters of the excitation signal.
Parameters | Numerical value |
---|---|
Amplitude | 100 N |
Waveform | Sine |
Sweep mode | Logarithmic |
Sweep range | 10∼500 Hz |
Sweep cycle | 40 s |
12 sinusoidal sweep tests were carried out with the change the position of the pair of eddy current displacement sensors from measure point D1 to D12. The displacement deviations between the baseplate and the constraining plate at D1∼D12 were collected by uT8916FRS-DY.
To verify the improvement of the vibration and damping characteristics of the steel plate (baseplate) by adding composite structure, a series of comparisons of the modal tests for steel plate (baseplate) and composite structure with different core thicknesses were carried out under different boundary conditions. The responses of the baseplate and composite structure were detected through 12 accelerometers. The response signals were recorded and processed by the use of uT8916FRS-DY in real time.
At the end of excitation, the time-frequency response function can be obtained by postprocessing with the time-frequency joint analysis technology [
The displacement deviations between the baseplate and the constraining plate at different measure points (D1 ∼ D12) were detected. Take data at measure point D1 as an example to analyze the relationship between displacement deviation and frequency (note: the thickness of EMWM is 4 mm).
Figure
Displacement response of the baseplate and the constraining plate under three different boundary conditions (measure point D1). (Note: the displacement direction is positive in the vertical direction and negative in the opposite direction). (a) C-C-F-F, (b) C-C-C-F, and (c) C-C-C-C.
Displacement deviation at measure points (D1 ∼ D12) under different boundary conditions. (unit:
C-C-C-C | C-C-C-F | C-C-F-F | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
First order | Second order | Third order | First order | Second order | Third order | First order | Second order | Third order | ||||||||||
MV | SD | MV | SD | MV | SD | MV | SD | MV | SD | MV | SD | MV | SD | MV | SD | MV | SD | |
D1 | 32.26 | 0.113 | 4.79 | 0.076 | 1.45 | 0.098 | 31.56 | 0.035 | 5.07 | 0.092 | 0.86 | 0.137 | 31.94 | 0.073 | 5.09 | 0.091 | 1.01 | 0.134 |
D2 | 32.31 | 0.147 | 5.04 | 0.154 | 1.62 | 0.142 | 31.49 | 0.027 | 5.22 | 0.107 | 0.82 | 0.144 | 31.86 | 0.182 | 5.04 | 0.143 | 0.99 | 0.097 |
D3 | 32.29 | 0.125 | 4.94 | 0.095 | 1.71 | 0.117 | 31.44 | 0.056 | 5.27 | 0.113 | 1.06 | 0.202 | 31.77 | 0.061 | 5.03 | 0.112 | 0.99 | 0.137 |
D4 | 32.22 | 0.118 | 4.97 | 0.082 | 1.32 | 0.134 | 31.45 | 0.043 | 5.33 | 0.086 | 1.13 | 0.183 | 30.72 | 0.062 | 5.11 | 0.083 | 1.12 | 0.146 |
D5 | 31.93 | 0.094 | 4.83 | 0.106 | 1.67 | 0.187 | 31.49 | 0.022 | 5.31 | 0.094 | 0.96 | 0.116 | 31.82 | 0.124 | 5.08 | 0.137 | 0.97 | 0.133 |
D6 | 32.18 | 0.157 | 5.22 | 0.233 | 1.75 | 0.143 | 31.55 | 0.016 | 5.41 | 0.083 | 1.27 | 0.134 | 31.79 | 0.153 | 5.02 | 0.224 | 1.08 | 0.212 |
D7 | 32.44 | 0.201 | 5.31 | 0.162 | 1.82 | 0.126 | 31.52 | 0.047 | 5.43 | 0.117 | 1.18 | 0.246 | 31.55 | 0.115 | 5.04 | 0.068 | 1.03 | 0.107 |
D8 | 31.97 | 0.193 | 5.09 | 0.066 | 1.87 | 0.132 | 31.49 | 0.028 | 5.13 | 0.104 | 1.21 | 0.209 | 31.23 | 0.092 | 4.95 | 0.047 | 1.15 | 0.093 |
D9 | 32.05 | 0.115 | 4.85 | 0.074 | 1.37 | 0.145 | 31.55 | 0.043 | 5.06 | 0.097 | 0.91 | 0.177 | 30.53 | 0.146 | 4.89 | 0.118 | 1.03 | 0.278 |
D10 | 32.12 | 0.174 | 4.92 | 0.096 | 1.58 | 0.184 | 31.48 | 0.034 | 5.17 | 0.105 | 0.92 | 0.092 | 30.76 | 0.128 | 4.91 | 0.132 | 0.89 | 0.139 |
D11 | 32.17 | 0.164 | 5.18 | 0.118 | 1.65 | 0.088 | 31.45 | 0.053 | 4.96 | 0.132 | 0.99 | 0.106 | 31.02 | 0.079 | 4.88 | 0.124 | 0.93 | 0.223 |
D12 | 32.09 | 0.247 | 5.11 | 0.125 | 1.51 | 0.139 | 31.44 | 0.064 | 5.34 | 0.109 | 0.87 | 0.102 | 30.44 | 0.134 | 4.76 | 0.083 | 0.86 | 0.064 |
Figure
The first three modal frequencies of the steel plate (baseplate) and composite structures with different core thicknesses under different boundary conditions. (a) First order, (b) second order, and (c) third order.
The natural frequency of vibration without damping
The natural frequency of vibration with damping
It can be seen from equations (
As illustrated in Figure
Figure
The damping ratios of the steel plate (baseplate) and composite structures with different core thicknesses under different boundary conditions. (a) First order, (b) second order, and (c) third order.
It can be seen from Figure
First three-order modal shapes of the baseplate and composite structures can be deduced from the vibration response of the baseplate and composite structures. It can be seen from Table
First three-order modal shapes of the baseplate and composite structures under different boundary conditions.
Boundary condition | Structure | 1st order | 2nd order | 3rd order |
---|---|---|---|---|
C-C-F-F | Steel plate | |||
Composite structure | ||||
C-C-C-F | Steel plate | |||
Composite structure | ||||
C-C-C-C | Steel plate | |||
Composite structure |
Frequency response curves (FRCs) for acceleration of the baseplate and composite structures with different core thicknesses under different boundary conditions were obtained by signal source and data acquisition system (uT8916FRS-DY) in real time. The FRCs for acceleration of the original steel plate (baseplate) (8 mm) at different measuring points are shown in Figure
The FRCs of steel plate (baseplate) under different boundary conditions at different measuring points. (a) C-C-F-F, (b) C-C-C-F, and (c) C-C-C-C.
The stiffness and damping factor are two key parameters that affect the vibration response of the structure. Figure
The FRCs of the baseplate and composite structures at 1st-order modal frequency under different boundary conditions (D1). (a) C-C-F-F, (b) C-C-C-F, and (c) C-C-C-C.
To reduce the vibration of the plate-like structure, a new composite structure was presented by adding EMWM layer and constraining plate. The damping performance of the EMWM was tested by a series of quasi-static compression tests. A dynamic test system was set up to verify that the displacement deviation between baseplate and constraining plate is sufficient to cause the energy dissipation of EMWM. The modal characteristics of the baseplate and composite structures with different core thicknesses under different boundary conditions were investigated. The main conclusions, which can be drawn from the conducted experiments, are as follows: The displacement deviations between the baseplate and constraining plate are sufficient to cause the energy dissipation of EMWM. Adding EMWM and constraining plate will reduce the modal frequency of the structure. Furthermore, the damping ratio of the structure would be significantly improved, and the amplitude of the FRF curve can be reduced. The larger the thickness of the core thickness is, the larger the damping ratio and vibration reduction performance of the composite structure are. The effect of EMWM on the vibration and damping characteristics of the composite structure under the boundary condition of C-C-C-C is not as obvious as that under the other boundary conditions.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
This work 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).
Displacement deviation at measure points (D1 ∼ D12) under different boundary conditions: (a) measure point D1; (b) measure point D2; (c) measure point D3; (d) measure point D4; (e) measure point D5; (f) measure point D6; (g) measure point D7; (h) measure point D8; (i) measure point D9; (j) measure point D10; (k) measure point D11; (l) measure point D12; (unit: