The dynamic properties of materials are important in various applications such as FEA modeling in crash testing of automotive vehicles. The natural frequencies of any system can be determined experimentally by FRF method using impact hammer. Further, these natural frequencies and FRF function can be utilized to obtain the dynamic stiffness and damping factor of the material. This methodology can be utilized to find out dynamic material properties of soft tissues such as liver, kidney etc. In the field of biomedical engineering it necessary to investigate human organ injury due to high speed impact or collision such as car accident. Smooth sil-910 having dynamic properties closely equal to human liver. So, the properties of human liver can be determined by finding dynamic properties of silicon rubber. Different samples of silicon material are prepared by keeping diameter constant and varying length and keeping length constant and varying diameter. The study of frequency as a function of length and diameter was carried out by using FFT analyzer. Frequency vs Area Ratio and frequency vs length graphs were plotted. As area ratio of specimen increases the frequency of specimen also increases and at certain point although area ratio increases frequency remains constant. Hence, in this case we find minimum area ratio for constant frequency. In second case as the length of specimen increases the frequency decreases and at threshold length it become constant. We can find optimum length for maximum frequency.

(b) Experimental Setup

It consists of following equipments

1. FFT

2. Impact Hammer

3. Accelerometer

4. Silicon sample

5. Preloads

Fig. 2 Experimental Setup layout

• The Force sensor is connected to the FFT through an impact hammer. It converts impact force into analogue signal.

• The accelerometer is of magnetic type and it will be attached on the preload to sense the vibration accelerations.

• Both the Impact hammer and Accelerometer having connections with FFT analyzer. And finally both devices will send the analogue signals to the FFT to get frequency response functions.

• The silicon samples are placed on support and preload is to be on the sample.

(c) Sample preparation

We are using silicon rubber as a sample material for test. Silicon samples have prepared into two forms as below

• Case 1 :- Constant Diameter and varying length

• Case 2 :- Constant length and varying Diameter

Detailed dimensions of silicon samples and preload pieces are shown in following tables with figure. The length of preload is kept constant for all pieces = 20 mm.

Table 1 Dimensions for silicon sample

Case 1 Parameter 1 2 3

Constant Diameter and varying length Diameter (mm) 25 25 25

Length (mm) 30 40 50

Case 2 Parameter 1 2 3

Constant length and varying Diameter Diameter (mm) 25 30 33

Length (mm) 50 50 50

Sr. No. 1 2 3

Area ratio 1:1 1:2 1:2.5

Diameters (mm) 25 12.5 10

30 15 12

33 16.5 13.2

(c)Procedure

• At first all the equipments are arranged as per set up. In first case we make a test on silicon samples of varying length and constant diameter

• When we made a impact on a pre-load which is mounted on a silicon sample with the help of impact hammer.

• At the tip of the impact hammer there is force sensor which senses the force value and it gives idea to give how much forced can be applied on the pre-load to get optimum vibration.

• The natural frequency of the silicon sample plus preload is sensed by accelerometer in terms of acceleration.

• And the signals coming from force sensor and accelerometer is send to FFT analyzer and it gives resonance frequency.

IV. RESULTS AND DISCUSSION

Table 4: Case No. 1- Constant Diameter Length varying

Sr.No. Area Ratio Frequency(Hz)

1 1 10.5

2 2 11.5

3 2.5 12

4 3 12.4

5 3.5 12.8

6 4 13.1

7 4.5 13.1

Frequencies for respective area ratio in case of constant diameter is shown in table no. 4, it shows that after area ratio 4 frequencies remain constant. Whereas table no.5 shows frequencies for respective length of specimen in case of constant length, which shows frequency become constant after length of specimen 80mm.

Fig. 6 Graph of Frequency vs Area Ratio

Summary:

From the graph it shows that as area ratio of silicon sample increases the frequency of silicon samples also increases .At certain point area ratio (AR=4) increases frequency remains constant

Table 5: Case No. 2 - Constant Length, Diameter varying

Sr.No. Length(mm) Frequency(Hz)

1 20 22.5

2 30 17

3 40 13

4 50 11.4

5 60 10

6 70 9.5

7 80 9.2

Fig. 7 Graph of Frequency vs Length

Summary:

From graph it shows that as length of silicon sample increases, the frequency of silicon sample decreases at the threshold length(L=80mm) it become constant.

Since the cross sectional areas of the silicon sample in our study experiment were significantly larger than that of the preload used in our experiment, an effective value for the cross sectional area was found with the help of graphs. The value of cross sectional area of silicon sample is four times the preload based on the result obtained in our experiments performed with silicon samples. For the effective length, the threshold length is obtained by the graph (length =80mm). From the case 1 result it shows that with increase in area ratio frequency increases that means material having more stiffness

V. CONCLUSION

From the available literature survey we inspired to study frequency dependent material properties of viscoelastic materials. We decided to test a silicon samples to find out its frequency dependent properties. We carried out tests on different dimensions of silicon samples and have got results from FFT Analyzer. We found that there is nonlinear behavior of material properties against frequency. In this case we have plotted two graphical nature such that Area ratio vs Frequency and Length vs Frequency of silicon samples.

Finally from graphical nature we conclude that as area ratio of specimen increases the frequency of specimen also increases and at certain point although area ratio increases frequency remains constant. Hence, in this case we find minimum area ratio for constant frequency. And in second case as the length of specimen increases the frequency decreases and at threshold length it become constant. We can find optimum length for maximum frequency. As we know that the smooth silicon, which is frequently used in movie industries for modeling Aliens, making mask, and replicating the human parts like arm, hand even face hence we can use this phenomenon in biomedical soft tissues.

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