HOME WORK II:

Determination of the modal parameters of the structure

T.Arriessa Sukhairi

(108013235855)

Advanced Control Methods for Adaptive Mechanical Systems

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The experimental modal analysis in 20 measurements using shaker modal testing. Shaker is

fixed at point 1 and accelerometer is rowing from point 1 to 20 (see figure 1).

Figure 1. Clamped cantilever beam with measurement points

Tasks:

1. Describe the measurement procedure.

On the Class room we do the experiments by using Shaker Modal Testing. A shaker is

a device that excites the structure according to its amplified input signal. The shaker

armature is attached to the body to be tested by a stinger. The force transducer is placed

between the shaker and the structure to obtain the excitation force. For vibration exciter

(shaker) excitation, the excitation point is fixed and is used as the reference position,

while the response accelerometer is moved around on the structure.

The excitation force from a vibration exciter is measured by a force transducer, and the

resulting signal is supplied to one of the inputs. Consequently, the frequency response

represents the structure’s accelerance since the measured quantity is the complex ratio of

the acceleration to force, in the frequency domain. The response is measured by an

accelerometer or laser – vibrometer, and the resulting signal is supplied to another input.

We set some gain values and time for input of the experiments. Then, the responses will

appear in the Monitor. Then, safe the data and move the accelerometer to calculate the

next point. A typical instrumentation set-up is illustrated in Fig.2.

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Figure 2. An instrumentation set-up provided by a vibration exciter

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2. Import the data from PULSE software into Matlab.

Click Import data, in MATLAB interface.

Select the file that we are going to input.

Input into workspace.

3. Determine and draw the mode shapes for the first four banding modes.

After we import our data from PULSE then we calculate the Amplitude by using the

formula

𝐴𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 = √𝑅𝑒2 + 𝐼𝑚2

Where:

Re : Real Part

Im : Imaginary Part

Then, we plot the frequency response graphic as can been seen in figure3.

Figure 3. Frequency responses for measurement 7

Then, we plot the mode shape by using the frequency response in the imaginary

part and the frequency. For the measurement 7 can be seen at the picture 4. And if

we combine all of the 20 measurement then we can see the banding mode shape

of the cantilever beam as shown in the figure 5.

Advanced Control Methods for Adaptive Mechanical Systems

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Figure 4. Mode Shape at Measurement 7

Figure 5. Mode Shape Cantilever Beam

4. Summarize your calculation and measurement results in a written report and Matlab

file (*.m ).

In the calculation we need to find the value of f1, f2, and fi. by using the figure 3 we

can determining the resonance frequency. We can observe this value from the

graphic, however we need to find the value of Xmax and 𝑋𝑚𝑎𝑥

√2 as shown in the

figure 6. Then after we found the value, observe again the figure 3 and take the

value for using to find the modal damping. For measurement 7 I got the value:

Advanced Control Methods for Adaptive Mechanical Systems

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i fi1 fi2 fi

1 11.05; 11.95 11.5

2 92.58 97.20 94.5

3 281.2 289.8 285

Table 1. The resonance frequency

Figure 6. Determining the resonance frequency and the modal damping

For the damping ratio can be calculated by using the formula:

Where:

: damping ratio

: the frequency bandwidth between the two half power points

: the i-th resonance frequency

After the calculation I get the value for the damping ratio:

1 0.03913

2 0.02444

3 0.01509

Table 2. Damping Ratio