13.5. Modal Analysis Technique

Try these first

1. 1.

   What are modal coordinates?

   Hint

   Think about how we express displacements for simplification.

2. 2.

   What type of equations does modal analysis create?

   Hint

   Remember the term 'SDOF' for simplification.

3. 3.

   What does the modal analysis technique primarily aim to do?

   • Decouple equations
   • Increase complexity
   • Enhance damping
   • None of the above

   Hint

   Consider the purpose of the technique.

4. 4.

   True or False: Modal coordinates express the motion of a system in terms of mode shapes.

   • True
   • False

   Hint

   Recall the terms we learned.

5. 5.

   A three-degree-of-freedom spring-mass system is defined with stiffness and mass matrices. derive the modal equations for this system and explain each transformation step.

   Hint

   Identify your main variables and remember to express displacements correctly.

6. 6.

   Calculate the modal response of a building subjected to an earthquake. You are given the natural frequencies and mode shapes. Detail your approach and assumed inputs.

   Hint

   Remember to factor in the input forces discretely for each mode.