11.6. Modal Analysis of Undamped MDOF Systems

Try these first

1. 1.

   What does MDOF stand for?

   Hint

   Think about degrees of freedom in mechanical systems.

2. 2.

   Define mode shapes in the context of dynamic analysis.

   Hint

   Consider how systems move when they vibrate.

3. 3.

   What is the primary purpose of modal analysis in MDOF systems?

   • To simplify structural design
   • To analyze dynamic behavior
   • To calculate loads

   Hint

   Think about what modal analysis reveals about structures.

4. 4.

   True or False: Each mode shape corresponds to a unique natural frequency.

   • True
   • False

   Hint

   Consider how vibrations are characterized.

5. 5.

   Given an MDOF structure with three modes, derive the basic form of the equations of motion when no damping is present. Assume mass and stiffness are known.

   Hint

   Use the natural frequency definitions and moment balance.

6. 6.

   Analyze how the modal responses would change if one of the mode shapes has a significantly higher natural frequency. What impact does this have on the total dynamic response?

   Hint

   Consider the principle of resonance and mass participation.