16.3. Mathematical Modeling of MDOF Systems

Try these first

1. 1.

   What is lumped mass idealization?

   Hint

   Think about how we model forces in a building.

2. 2.

   What does the mass matrix [M] represent?

   Hint

   Focus on the structure's floors and their contribution to mass.

3. 3.

   What does the mass matrix [M] represent in an MDOF system?

   • Distribution of forces
   • Distribution of mass
   • Velocity of each mass

   Hint

   Which matrix talks about weights?

4. 4.

   True or False: The stiffness matrix [K] is a diagonal matrix.

   • True
   • False

   Hint

   Consider the nature of the structure.

5. 5.

   Given a structure with 4 floors, each with mass 1000 kg, and a stiffness of 10000 N/m for each floor, set up the mass and stiffness matrices.

   Hint

   Think about how mass and stiffness are distributed.

6. 6.

   Analyze how damping affects an MDOF system subjected to harmonic loading.

   Hint

   Recall the significance of energy loss during oscillations.