11.5. Normalization of Mode Shapes

Try these first

1. 1.

   What is the purpose of normalizing mode shapes?

   Hint

   Think about why we adjust values in mathematical functions.

2. 2.

   What does mass normalization require?

   Hint

   Review the conditions for mass normalization.

3. 3.

   What is the main purpose of normalizing mode shapes?

   • To increase complexity
   • To simplify computation
   • To confuse engineers

   Hint

   Think about the reasons for adjusting values in mathematics.

4. 4.

   True or False: Stiffness normalization and mass normalization are identical.

   • True
   • False

   Hint

   What aspects do each method pertain to?

5. 5.

   Given a 3-DOF system with mode shapes and their corresponding mass and stiffness matrices, normalize the mode shapes using both methods and discuss the outcomes.

   Hint

   Set up the equations based on mass and stiffness for normalization.

6. 6.

   Identify a real-world application where normalization of mode shapes is critical. Discuss the implications of incorrectly normalized shapes in that context.

   Hint

   Reflect on structures impacted by seismic events and the degree of accuracy needed.