12.5. Forced Vibration and Modal Analysis

Try these first

1. 1.

   Define forced vibration in your own words.

   Hint

   Think about systems responding to external conditions.

2. 2.

   What do the terms M and K represent in the forced vibration equation?

   Hint

   Consider the definitions of mass and stiffness.

3. 3.

   What does the equation Mx¨ + Kx = F(t) represent?

   • Static analysis
   • Free vibration
   • Forced vibration

   Hint

   Focus on the definitions of vibration.

4. 4.

   True or False: Modal analysis allows for the consideration of all modes simultaneously.

   • True
   • False

   Hint

   Think about the term 'uncoupled'.

5. 5.

   Consider a 2-DOF system subjected to a harmonic force F(t) = F0sin(ωt). Derive the equations governing this system in terms of modal coordinates.

   Hint

   Identify the node's natural frequencies along with the force frequency.

6. 6.

   Analyze the impact of increasing the coupling stiffness in the forced vibration of a two-story building modeled as a 2-DOF system.

   Hint

   Predict changes using your knowledge of stiffness relationships.