16.4.2. Orthogonality of Mode Shapes

Try these first

1. 1.

   What does the term 'mode shape' refer to?

   Hint

   Think about how structures move.

2. 2.

   Define orthogonality in terms of vectors.

   Hint

   Consider how two vectors might not affect each other.

3. 3.

   What does the orthogonality of mode shapes imply?

   • They affect each other's energy
   • They do not interfere with each other
   • They are identical

   Hint

   Remember how each mode operates uniquely.

4. 4.

   Is the following statement true or false? 'Orthogonality helps in simplifying dynamic analysis.'

   • True
   • False

   Hint

   Consider the benefits of independent calculations.

5. 5.

   You have two mode shapes with a given mass matrix. Calculate if they are orthogonal, using {ϕ}_1 and {ϕ}_2 with [M] given as a diagonal matrix. What does the result indicate?

   Hint

   Perform matrix multiplication and check the outcome.

6. 6.

   Explain how the lack of orthogonality would affect a skyscraper's response to an earthquake and propose a method to address this complication.

   Hint

   Think about simulation tools used in structural analysis.