Study on dynamic characteristic of closed-cell aluminum foam

2.1. Feature parameters

The samples were made by melt foaming method and incised by wire-electrode cutting method. The sample size, outside diameter is Ø440 mm, inside diameter is Ø280 mm and the height is unequal.

Porosity is an important parameter to describe the closed-cell aluminum foam. The measurement method of porosity is divided into weighing method and microscopic method. For its simple and high precision, weighing method is commonly used. According to the dimension and weight of the sample, using the Eq. (1) to calculate the porosity:

In which, $m$ and $V$ are the mass and volume of the sample, respectively, ${\rho }_s$ is the density of matrix material.

The measurement of pore parameters mainly includes direct method and indirect method that using the software to analysis the surface topography of the sample [19]. In this article, we applied a new and simple method to measure the pore parameters. It has the advantages of low cost and high precision. The main equipment is digital camera and the main software is Photoshop, Matlab and Image-Pro Plus. The basic procession is shown in Fig. 1.

Fig. 1The basic procession

2.2. Dynamic characteristic test

The dynamic characteristic was performed by experimental modal analysis and FEM. As shown in Fig. 2, the whole testing system composed by four parts; suspension part, shaking part, testing part and software analysis part. The suspension part includes rigid bracket and elastic soft cord to simulate the free boundary condition. The shaking part is impact hammer which is commonly used in the single-input single-output (SISO) modal analysis to produce pulse signal. The testing part is PCB accelerometer and high-speed data acquisition system. The software analysis part is Virtual lab/Modal Analysis software.

Fig. 2The testing system

In the modeling process, the model is simplified to octagon with 48 nodes and ignores the mounting holes, as shown in Fig. 3. In which point 1:1 to 1:24 is the master node and the rest is the slave node. The PCB acceleration sensor is installed in the 1:3 points. During the experiment, using the force hammer which installed rigid head to beat the other master node, every node beats at least three times. The related experimental parameters as shown in Table 1.

Fig. 3The geometric model

MAC was used to test the linear independence of each order. MAC is a good tool to evaluate the modal vector space angle. It can be expressed as follows:

where ${\phi }_i$and ${\phi }_j$ are the corresponding freedom of the $i$ and $j$ order calculation mode, respectively. The smaller of the off-diagonal matrix is the better of the independence of each calculation mode.

In this article, we also used the ABAQUS software to give a modal analysis in order to better verify the testing results. The basic steps of modal analysis in ABAQUS include modeling, select the analysis type, set the corresponding parameters, applying the boundary conditions, solve and results post processing. The parameters used in the simulation are shown in Table 2.

3.1. Feature parameters analysis

Table 3 shows the feature parameters of aluminum foam. It can be found that the porosity is among 81.9 % to 86.42 %, the relative density is among 0.136 to 0.181, the average diameter is among 2.42 to 3.23 mm.

3.2. Experimental modal analysis

3.2.1. Results and validation

In this article, we analyzed the first six orders. As shown in Fig. 4 is the MAC of each sample. Through the MAC it can be found that except the diagonal correlation is 100 %, the other off-diagonal correlation is fewer than 10 % and mostly fewer than 5 %. According the above criteria of MAC, it can be found that the node configuration is reasonable, and each order modal has higher orthogonality.

Fig. 4Modal assurance criterion

a) Sample one

b) Sample two

3.2.2. Discussion of experimental modal results

(1) Relationship between damping ratio and porosity.

As shown in Fig. 5 is the result of damping ratio of each sample. It can be seen from Fig. 5 each order damping ratio increases with the increase of porosity, the damping ratio and porosity is positively correlated. But in some orders the damping ratio decreases with the increase of porosity for the manufacturing defect.

Fig. 5Relationship between damping ratio and porosity

a) Sample one

b) Sample two

(2) Relationship between natural frequency and porosity.

Material’s vibration damping performance and damping ratio are closely related, but there is another important factor that affects the vibration damping performance is the natural frequency of the sample. As shown in Fig. 6, it can be found that the natural frequency of each order decreases with the increase of porosity and increases with the increase of height of the sample. In this experiment, the sample’s axial dimension is less than the radial dimension, the stiffness of axial increases greater than the increase of mass, its natural frequency is increased with the increase of height.

Fig. 6Relationship between natural frequency and porosity

a) Sample one

b) Sample two

3.3. Comparison between experiment and FEM

By comparing the simulation results and experimental results can make a mutual authentication between the two methods. The results are shown in the Table 4. As it can be seen the simulation results can be good fit with the testing results. So, in the next study, we can use the FEM to study its dynamic characteristic.