15.3.1. Orthogonality of Mode Shapes

Try these first

1. 1.

   Define mode shape in your own words.

   Hint

   Think about how structures move when disturbed.

2. 2.

   What does it mean for two mode shapes to be orthogonal?

   Hint

   Consider vectors that point in different directions.

3. 3.

   What does the orthogonality of mode shapes allow in structural analysis?

   • Interference of modes
   • Independent analysis of modes
   • Increased complexity

   Hint

   Think about how vectors can behave in an analysis.

4. 4.

   True or False: Mode shapes are orthogonal with respect to the mass matrix.

   • True
   • False

   Hint

   Consider the definition of orthogonality.

5. 5.

   Using a 2-DOF system as an example, demonstrate how to establish the orthogonality of two mode shapes mathematically.

   Hint

   Coordinate the analysis using the properties of eigenvectors.

6. 6.

   In designing a building, how would you illustrate the importance of stiffness orthogonality when faced with uneven mass distribution?

   Hint

   Think about how sway patterns might be altered with irregular mass distributions.