1.8.2. Mode Shapes and Natural Frequencies

Try these first

1. 1.

   What is the eigenvalue problem?

   Hint

   Think about how we analyze structures.

2. 2.

   Define natural frequency.

   Hint

   Remember, it's about oscillation without external forces.

3. 3.

   What is the primary function of the eigenvalue problem in structural dynamics?

   • To find the mass of a structure.
   • To determine natural frequencies and mode shapes.
   • To calculate load-bearing capacities.

   Hint

   Recall what we've discussed about the role of eigenvalues.

4. 4.

   True or False: Mode shapes can reveal how different parts of a structure vibrate relative to each other.

   • True
   • False

   Hint

   Think about the significance of deformation patterns.

5. 5.

   Given a two-degree-of-freedom system with specific mass and stiffness values, derive the natural frequencies and mode shapes.

   Hint

   Look for cyclic patterns or symmetric properties in your matrices.

6. 6.

   Explain how you would use modal analysis for a building designed in a seismic zone. What considerations did you take into account?

   Hint

   Apply knowledge from previous lessons on resonance and reinforcement.