1.8. Multi-Degree of Freedom (MDOF) Systems

Try these first

1. 1.

   What does MDOF stand for?

   Hint

   Consider how it relates to the dimensions of motion.

2. 2.

   Define the mass matrix in the context of MDOF systems.

   Hint

   It's related to how much mass affects motion.

3. 3.

   What is the primary equation governing MDOF systems?

   • [M]{ẍ} + [C]{x˙} + [K]{x} = {F(t)}
   • [K]{x} + [M]{x} = 0
   • [C]{x} = {F(t)}

   Hint

   Look for the equation combining all key system properties.

4. 4.

   True or False: Mode shapes represent how a system vibrates at its natural frequencies.

   • True
   • False

   Hint

   Think about what happens during free vibrations.

5. 5.

   A three-story building is modeled as a 3-DOF system. Given the mass matrix [M] as diag(2000, 1500, 1000) kg and the stiffness matrix [K] as diag(5000, 4000, 3000) N/m, determine the estimation of natural frequencies.

   Hint

   Remember to formulate the matrix to solve for characteristic polynomial.

6. 6.

   Analyze the impact of increasing damping in an MDOF system on its mode shapes and natural frequencies. What criteria will you consider?

   Hint

   Consider how damping affects dynamic stability and frequency response.