32.4. Response of Multi-Degree-of-Freedom (MDOF) Systems

Try these first

1. 1.

   What does MDOF stand for?

   Hint

   Think about degrees of freedom in structural movement.

2. 2.

   What is the purpose of the mode shapes in MDOF analysis?

   Hint

   Consider how structures behave under different types of loads.

3. 3.

   What is the equation of motion for MDOF systems?

   Hint

   Remember the matrices involved in structural dynamics.

4. 4.

   True or False: The mode shapes in MDOF systems are usually affected by each other.

   • True
   • False

   Hint

   Think about why we want independent behaviors in dynamics.

5. 5.

   Given a three-story frame structure with known mass and stiffness, derive the equation of motion for the MDOF system.

   Hint

   Focus on how each part contributes to the entire system.

6. 6.

   Using the matrix method, explain how you would calculate the mode shapes for a given MDOF system.

   Hint

   Recall the relationship between eigenvalues, eigenvectors, and physical motion described in modal analysis.