Report on Natural Frequency, Mode Shape and Model Analysis In FEM

The natural frequency is the frequency at which a system naturally vibrates once it has been set into motion. In other words, the natural frequency is the number of times a system will oscillate (move back and forth) between its original position and its displaced position, if there is no outside interference.

Natural Frequency of a Vibrating Beam Supplies:
1. Flexible lightweight fishing rod or other flexible rods. It is very important that the rod be highly flexible.
2. Several objects of various weights that can be attached to the rod, such as a tennis ball, heavy fishing sinkers, heavy bolts or nuts, etc. These objects should weigh more than the rod to provide the most successful experiments.
3. Table to which the rod can be attached.
4. C-clamp for fastening the rod to the edge of the table.
5. Stopwatch or clock with a capability to indicate seconds.

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1. Clamp the largest end of the fishing rod to the table.
2. Pull the end of the rod downward, and then release it. If the rod moves slowly enough, count the number of oscillations (rod moving through a complete cycle and back to release point) that occur in 30 seconds. The frequency is the number of oscillations divided by seconds.
3. Now attach one of the weights to the free end of the rod, and again pull it down then release it. Count the number of oscillations and divide by the time to get the frequency.
4. Repeat step 3 for different tip weights. Plot frequency vs. tip weight. How does frequency change with the weight?
5. Calculate the natural frequency and compare to the experiment described in steps 3 and 4 using the following procedure:
(a). Place a yardstick near the free end of the fishing rod, with one end of the yardstick resting on the floor.
(b). Attach one of the weights to the end of the fishing rod and measure the distance (x) that the end of the rod moves downward.The stiffness k equals the weight of the tip mass divided by the distance the end of the rod moves.




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