17.5. Normalization of Mode Shapes

Try these first

1. 1.

   What does normalization of mode shapes ensure?

   Hint

   Think about how they are related mathematically.

2. 2.

   What is the significance of the mass matrix in dynamic analysis?

   Hint

   Consider what factor affects motion.

3. 3.

   What is the purpose of normalizing mode shapes?

   • To simplify dimension calculations
   • To standardize contributions to mass
   • To disregard mode shape effects

   Hint

   Think about how each mode shape contributes in calculations.

4. 4.

   True or False: Mode shapes do not influence the seismic response of structures.

   Hint

   Recall the relationship between mode shapes and dynamic behavior.

5. 5.

   Given a mass matrix, derive the normalized form of the corresponding mode shapes and discuss the implications.

   Hint

   Recall the properties of mass when upon mode shapes.

6. 6.

   Analyze how changing the mass distribution affects the normalization of mode shapes and the resulting natural frequencies.

   Hint

   Consider real-world examples like high-rises with varying floor weights.