11.7. Equations of Motion for Damped MDOF Systems

Try these first

1. 1.

   What is the equation for a damped MDOF system?

   Hint

   Recall the components involved in the equation.

2. 2.

   Define the modal damping ratio.

   Hint

   Consider what quantifies the decay of oscillations.

3. 3.

   What does the damping matrix [C] represent?

   • Energy dissipation
   • Structural mass
   • External forces

   Hint

   Think about what effects damping has on motion.

4. 4.

   True or False: The equations of motion for damped MDOF systems can be similar to those for damped SDOF systems.

   • True
   • False

   Hint

   Remember the form of the differential equations.

5. 5.

   Draft the equation of motion for a damped 3-DOF system with given mass [M] and stiffness [K] matrices, assuming classical damping is present.

   Hint

   Break down your problem: initiate with defining [C] using [M] and [K].

6. 6.

   Calculate the modal damping ratios for a system defined by its natural frequency of 2 Hz and a given damping coefficient.

   Hint

   Identify your variables for mass and stiffness within the problem.