8.15. Harmonic Excitation in Multi-Degree-of-Freedom (MDOF) Systems

Try these first

1. 1.

   What are the governing equations for MDOF systems?

   Hint

   Consider the matrix notation used in dynamic analysis.

2. 2.

   Define modal analysis in your own words.

   Hint

   Think about how we simplify systems for better understanding.

3. 3.

   What are the components of the governing equations in MDOF systems?

   • Mass
   • Damping
   • Stiffness
   • Force
   • Speed
   • Motion
   • Load
   • Stress
   • Strain

   Hint

   These components are related to the properties of the system.

4. 4.

   True or False: Modal analysis is used to combine responses of individual modes to understand an entire system's behavior.

   • True
   • False

   Hint

   Think about the purpose of breaking down a complex system into simpler parts.

5. 5.

   Given a 5-story building modeled as an MDOF system, describe how you would approach the modal analysis to ensure safety during an earthquake.

   Hint

   Think about the steps of identifying natural frequencies and how they relate to design choices.

6. 6.

   A bridge experiences significant harmonic excitation at certain frequencies. Detail an approach using governing equations and modal analysis to mitigate this issue in its design.

   Hint

   Consider how the interactions between mass, damping, and stiffness can alter response characteristics.