8.15.1. Governing Equations

Try these first

1. 1.

   Define the term 'Multi-Degree-of-Freedom System'.

   Hint

   Think about how many ways it can move.

2. 2.

   What does the stiffness matrix [K] represent?

   Hint

   Consider what is restoring the system back to its position.

3. 3.

   What is the main purpose of the mass matrix in the governing equations of a MDOF system?

   • To store energy
   • To represent inertia
   • To reduce vibrations

   Hint

   Think about how mass affects motion.

4. 4.

   True or False: The stiffness matrix indicates how much the system resists deformation.

   • True
   • False

   Hint

   What happens when you stretch a spring?

5. 5.

   Given a mass matrix [M] of a system and its respective damping and stiffness matrices, compute the steady-state response under harmonic excitation.

   Hint

   Make sure to consider how the matrices interact with the force vector.

6. 6.

   Analyze how varying stiffness in an MDOF system impacts the overall system response. Discuss potential outcomes.

   Hint

   Think about how a stiffer system would behave differently than a softer one.