12.6. Damped 2-DOF Systems

Try these first

1. 1.

   What is the general equation of motion for a damped 2-DOF system?

   Hint

   Consider what terms we need for damping effects in a dynamic system.

2. 2.

   Define Rayleigh damping.

   Hint

   Think about how damping relates to mass and stiffness.

3. 3.

   What is the equation of motion for a damped 2-DOF system?

   Hint

   Remember the prime factors: mass, damping, and stiffness.

4. 4.

   Is Rayleigh damping proportional to mass?

   • True
   • False

   Hint

   Think about how energy dissipation relates to mass in structures.

5. 5.

   Given a damped 2-DOF system with m1 = 500kg, m2 = 300kg, and k1 = 40000N/m, k2 = 20000N/m, k12 = 10000N/m. Calculate the natural frequencies with damping matrix as C = 0.05M + 0.07K.

   Hint

   Use the relationship between the eigenvalues and the eigenvectors from the modified matrices.

6. 6.

   In a real-life scenario, how would damping affect the design of a skyscraper? Discuss considerations in the context of earthquake resistance.

   Hint

   Consider the building's height and flexibility in your answer.