13.3. Free Vibration Analysis of MDOF Systems

Try these first

1. 1.

   What are the two main assumptions in free vibration analysis of MDOF systems?

   Hint

   Think about what characteristics simplify the analysis.

2. 2.

   Express the assumed solution for free vibrations mathematically.

   Hint

   What form describes oscillation over time?

3. 3.

   What is the first assumption in free vibration analysis?

   • Presence of damping
   • No external force
   • External vibrations

   Hint

   Consider what enables the analysis of natural motion.

4. 4.

   True or False: Mode shapes correspond to natural frequencies.

   • True
   • False

   Hint

   Think about how they are linked in analysis.

5. 5.

   Given a system with specific mass and stiffness matrices, derive the characteristic equation and solve for ω².

   Hint

   What mathematical operation will you use to determine the roots of your characteristic equation?

6. 6.

   Discuss the implications of ignoring damping in real-world systems. How might this affect your vibrational analysis?

   Hint

   Think about how real structures behave during events.