12.16. MATLAB/Computational Implementation

Try these first

1. 1.

   What is the primary function of the mass matrix in a 2-DOF system?

   Hint

   Think about how mass affects motion.

2. 2.

   What command do we use in MATLAB to solve the eigenvalue problem?

   Hint

   This command is short for a mathematical term often used in linear algebra.

3. 3.

   What command is used to solve the eigenvalue problem in MATLAB?

   • eig
   • solve
   • find

   Hint

   Look for the command related to eigenvalues.

4. 4.

   True or False: The mass matrix affects how the system responds to external forces.

   • True
   • False

   Hint

   Think about how mass influences movement.

5. 5.

   A structure has a mass matrix of M = [500 0; 0 1500] and a stiffness matrix of K = [20000 -5000; -5000 30000]. Compute the natural frequencies.

   Hint

   Remember to inspect the diagonal of the D matrix.

6. 6.

   Consider a 2-DOF system under harmonic excitation. Write a MATLAB script segment to simulate the system response over time for given force inputs.

   Hint

   Utilize the previously defined matrices and modal responses.