13.4. Properties of Normal Modes

Try these first

1. 1.

   What does the orthogonality property of normal modes imply?

   Hint

   Think about how two different modes would behave geometrically!

2. 2.

   Why is normalization important in modal analysis?

   Hint

   Consider why having a uniform scale would be beneficial.

3. 3.

   What does orthogonality in normal modes imply?

   • They affect each other
   • They are independent
   • They are coupled

   Hint

   Reflect on how distinct shapes behave separately.

4. 4.

   True or False: Normalization is irrelevant in modal analysis.

   • True
   • False

   Hint

   Think about simplifying equations in mathematics.

5. 5.

   Given a multi-degree-of-freedom system with specified mode shapes and participation factors, derive the total response under a known dynamic load. Consider different damping ratios in your evaluation.

   Hint

   Remember to consider how damping ratios can alter mode contributions effectively.

6. 6.

   Analyze a case where the completeness fails due to a non-linear response in a real structure. Provide an extensive explanation of the implications and potential solutions.

   Hint

   Think about dynamic loads that could change behavior unexpectedly.