13.7. Computational Aspects

Try these first

1. 1.

   What is the role of the mass matrix in structural analysis?

   Hint

   Think about what controls the dynamics of motion.

2. 2.

   What is a numerical eigenvalue solver?

   Hint

   How do we find natural frequencies mathematically?

3. 3.

   Why is matrix algebra important in normal mode analysis?

   • A) It simplifies structural formulas.
   • B) It allows for complex systems to be modeled.
   • C) It eliminates the need for calculations.
   • D) It makes the process slower.

   Hint

   Think about how we represent multiple degrees of freedom.

4. 4.

   True or False: The accuracy of the stiffness matrix does not impact the analysis results.

   • True
   • False

   Hint

   Recall how mass and stiffness are related to natural frequencies.

5. 5.

   You have a two-degree-of-freedom system with known mass and stiffness values. Calculate the natural frequencies and mode shapes using matrix methods. Provide step-by-step reasoning.

   Hint

   Use the determinant to simplify your calculations.

6. 6.

   Consider a scenario where the mass distribution changes significantly in a structure. Analyze how this may influence the structure's dynamic response and determine what steps could be taken to mitigate adverse effects.

   Hint

   Think about how the ground vibrations might interact with the building's new dynamics.