12.9. Numerical Example

Try these first

1. 1.

   What are the stiffness values for the springs in our 2-DOF system?

   Hint

   Think about the spring constants given in the example.

2. 2.

   How many masses are there in the 2-DOF system?

   Hint

   Refer to the mass details outlined in the example.

3. 3.

   What is the primary role of the mass matrix (M) in a 2-DOF system?

   • To provide stiffness values
   • To represent the connection of loads and motions
   • To solve the eigenvalue problem

   Hint

   Think about what the mass matrix primarily establishes in a dynamic system.

4. 4.

   True or False: The mode shapes are always orthogonal in a 2-DOF system.

   • True
   • False

   Hint

   Recall the properties of mode shapes regarding their relationships.

5. 5.

   In a given 2-DOF system, the masses are doubled while stiffness remains constant. How does this affect the natural frequencies? Explain the relationship.

   Hint

   Refer to the frequency formula involving mass and stiffness.

6. 6.

   Consider a scenario where the coupling stiffness k12 is significantly increased. Describe the expected effects on the mode shapes and frequencies.

   Hint

   Think about how stronger connections impact vibration dynamics.