13.8. Examples and Case Studies

Try these first

1. 1.

   What defines a two-degree-of-freedom system?

   Hint

   Think of how many ways it can move.

2. 2.

   What are participation factors?

   Hint

   They help understand the importance of modes in vibration.

3. 3.

   What is the significance of natural frequencies in a system?

   • They determine the stiffness
   • They represent the system's preferred oscillation frequency
   • They are irrelevant to dynamic analysis

   Hint

   Consider the frequency at which the system will vibrate the most efficiently.

4. 4.

   True or False: In a two-degree-of-freedom system, both modes can oscillate independently.

   • True
   • False

   Hint

   Remember the definition of two degrees of freedom.

5. 5.

   A two-degree-of-freedom system has a mass matrix M = [[2, 0], [0, 3]] and a stiffness matrix K = [[6, -2], [-2, 5]]. Calculate the natural frequencies.

   Hint

   Use the determinant to create your characteristic equation.

6. 6.

   For a three-storey shear building, explain how you would determine which modes are significant for seismic analysis and how you would approach the modal validation.

   Hint

   Look at how much each mode contributes to the overall movement.