15.6.2. Cantilever Beam

Try these first

1. 1.

   What does a cantilever beam look like during the first mode of vibration?

   Hint

   Think about the shape of a wave.

2. 2.

   What is a mode shape?

   Hint

   Relate it to how structures respond when they vibrate.

3. 3.

   What kind of shape does the first mode of a cantilever beam resemble?

   • Square
   • Circle
   • Sine waveform

   Hint

   Think of the simple wave motion.

4. 4.

   True or False: The second mode shape of a cantilever beam has a single curvature.

   • True
   • False

   Hint

   Focus on how the vibration alters shape.

5. 5.

   A cantilever beam is used in a structure subject to dynamic forces. How would you evaluate if its design is sufficient for the second mode shape?

   Hint

   What happens when the frequency of external forces matches natural frequencies?

6. 6.

   Discuss the implications and potential failures that could occur if a cantilever beam design does not consider mode shapes.

   Hint

   Think about how ignoring vibrations could affect stability.