15. Mode Shapes

Try these first

1. 1.

   Define a mode shape.

   Hint

   Think about how structures move when disturbed.

2. 2.

   What does free vibration mean?

   Hint

   Consider what happens when you stop pushing a swing.

3. 3.

   What is the first mode shape typically associated with?

   • Localized motion
   • Global movement of the entire structure
   • Higher frequency oscillations

   Hint

   Think of how a building sways during an earthquake.

4. 4.

   True or False: Mode shapes are always normalized to have the same magnitude.

   • True
   • False

   Hint

   Think about how we often scale things to make them easier to analyze.

5. 5.

   Consider a cantilever beam with an uneven mass distribution. Calculate the first three mode shapes for this beam and discuss how an uneven mass may affect its dynamic behavior.

   Hint

   Utilize principles of vibration modes to evaluate the scenarios.

6. 6.

   Analyze the modal participation factors for a 3-DOF system subjected to seismic loading. How do you interpret these factors in terms of structural design?

   Hint

   Consider what it means for each mode's contribution to the response.