9.14. Extension to Multi-Degree-of-Freedom (MDOF) Systems

Try these first

1. 1.

   Define what an MDOF system is in your own words.

   Hint

   Think about structures and how parts can move independently.

2. 2.

   What do the matrices [M], [C], and [K] represent?

   Hint

   Consider the physical properties of structures.

3. 3.

   What does the matrix [M] in the MDOF equation represent?

   • A) Damping
   • B) Stiffness
   • C) Mass

   Hint

   Consider what mass contributes to in dynamic systems.

4. 4.

   True or False: The impulse response matrix H(t) relates the response of only one degree of freedom to a unit impulse.

   • True
   • False

   Hint

   Look at the definition of impulse response.

5. 5.

   Given a 3-DOF system with mass values of [1,2,1] kg and stiffness values of [4,3,4] N/m, derive the equations of motion and identify eigenvalues.

   Hint

   Use matrix representations to form the equations.

6. 6.

   Consider a structure modeled as a 2-DOF MDOF system subjected to an impulse. Explain how the system's total response can be calculated using modal analysis.

   Hint

   Recall the steps of modal analysis and response calculation.