16.14. Numerical Example: 2-DOF System

Try these first

1. 1.

   Define the mass matrix for a 2-DOF system with m1=5 kg, m2=10 kg.

   Hint

   Consider how mass is represented in matrix form.

2. 2.

   What does the stiffness matrix represent?

   Hint

   Think about the properties of the materials involved.

3. 3.

   What does the mass matrix in a 2-DOF system represent?

   • The stiffness of the system
   • The distribution of mass
   • The damping characteristics

   Hint

   Consider what defines the motion of each mass.

4. 4.

   Is the stiffness matrix in a 2-DOF system always symmetric?

   • True
   • False

   Hint

   Think about how stiffness in structures interacts.

5. 5.

   Consider a 2-DOF system with masses m1=12 kg and m2=8 kg. The stiffness matrix is given as [K] = [[30, -10], [-10, 20]]. Calculate the natural frequencies and corresponding mode shapes.

   Hint

   Use MATLAB or numerical methods for precise calculations.

6. 6.

   For the 2-DOF system, determine the response to an external seismic input defined by a force vector. Use modal superposition to articulate the total displacement.

   Hint

   Break down each mode's impact and ensure correct summation.