30.6.2. Vibration Analysis

Try these first

1. 1.

   What do eigenvalues represent in vibration analysis?

   Hint

   Think about what frequencies matter in design.

2. 2.

   What is the role of eigenvectors?

   Hint

   Consider how a structure deforms during vibrations.

3. 3.

   What does vibration analysis help to prevent?

   • Structural Damage
   • Resonance
   • Both

   Hint

   Consider the consequences of unchecked vibrations.

4. 4.

   True or False: Eigenvalues indicate how a structure deforms under load.

   • True
   • False

   Hint

   Think about what each term specifically relates to.

5. 5.

   A structure is undergoing analysis for dynamic loading. The mass and stiffness matrices have been determined. Derive the characteristic polynomial to find the eigenvalues.

   Hint

   Focus on the relationship between mass and stiffness.

6. 6.

   How might the eigenvalues of a poorly designed bridge affect its performance and safety during an earthquake?

   Hint

   Think about real-life cases of structural failures due to resonance.