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Merge pull request #11 from virtual-labs/testing
Responsive Simulator Added
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**AIM**: | ||
To find the damping (c) of the given beam. | ||
### Procedure | ||
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**PROCEDURE**: | ||
Begin the experiment by clicking the start experiment button. | ||
[<img src="./images/proc1.png" width="800" height="600" />](./images/proc1.png) | ||
<div style="text-align:left"> | ||
Click on the Simulation icon <img src="images/simulation.png" alt="Alt text" style="height:80px; width:80px;"> to view the simulation screen. | ||
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1. Find logarithmic decrement (δ) from displacement v/s time graph. The logarithmic decrement is defined as follows. | ||
[<img src="./images/proc2.png" width="150" height="75" />](./images/proc2.png) | ||
![Alt text](images/img1.png) | ||
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In order to view the variable section click on the Variable icon. <img src="images/var1.png" alt="Alt text" style="height:80px; width:80px;"> | ||
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Here x<sub>1</sub> and x<sub>n</sub> refer to the displacements at the first and nth peak in the displacement v/s time graph. | ||
The displacements at the peaks can be found using the location slider. | ||
[<img src="./images/proc3.png" width="800" height="600" />](./images/proc3.png) | ||
[<img src="./images/proc4.png" width="800" height="600" />](./images/proc4.png) | ||
![Alt text](images/img2.png) | ||
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2. Find the damping ratio (ζ) from the logarithmic decrement (δ). The damping ratio is given by | ||
[<img src="./images/proc5.png" width="150" height="75" />](./images/proc5.png) | ||
[<img src="./images/proc6.png" width="800" height="600" />](./images/proc6.png) | ||
Click on Play icon <img src="images/play1.png" alt="Alt text" style="height:80px; width:80px;"> to run the simulation and click on Pause icon <img src="images/pause.png" alt="Alt text" style="height:80px; width:80px;"> to stop it. | ||
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3. Find beam stiffness (k) N/m from Young's modulus (E), area moment of inertia (I) and length (L). The stiffness for different beams is given below | ||
[<img src="./images/proc7.png" />](./images/proc7.png) | ||
[<img src="./images/proc8.png" width="800" height="600" />](./images/proc8.png) | ||
Click on the graph icon <img src="images/graph1.png" alt="Alt text" style="height:80px; width:80px;"> to view the graph. | ||
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4. Find natural frequency (ω<sub>n</sub>) rad/s from ω<sub>d</sub> and ζ | ||
ω<sub>d</sub> can found from the FFT in the graph window. | ||
[<img src="./images/proc9.png" width="150" height="75" />](./images/proc9.png) | ||
[<img src="./images/proc10.png" width="800" height="600" />](./images/proc10.png) | ||
![Alt text](images/img4.png) | ||
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5. Find equivalent mass ( m<sub>eq</sub>) in kg from ω<sub>d</sub> and k. | ||
[<img src="./images/proc11.png" width="100" height="70" />](./images/proc11.png) | ||
[<img src="./images/proc12.png" width="800" height="600" />](./images/proc12.png) | ||
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6. Find critical damping (c<sub>c</sub> in Ns/m) from m<sub>eq</sub> and k. | ||
[<img src="./images/proc13.png" width="100" height="35" />](./images/proc13.png) | ||
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7. Find damping (c) Ns/m from c<sub>c</sub> and ζ. | ||
[<img src="./images/proc14.png" width="80" height="30" />](./images/proc14.png) | ||
[<img src="./images/proc15.png" width="800" height="600" />](./images/proc15.png) | ||
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**RESULT**: | ||
System damping c has been found. The basic concepts in free vibration of SDOF systems are covered. | ||
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[<img src="./images/proc16.png" width="800" height="600" />](./images/proc16.png) | ||
Click on the result icon <img src="images/result.png" alt="Alt text" style="height:80px;width:80px;"> to view the result tab | ||
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![Alt text](images/img3.png) | ||
</div> |
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