13.2. Concept of Mode Shapes and Natural Frequencies

Try these first

1. 1.

   Define natural frequency.

   Hint

   Think about vibrations in a structure.

2. 2.

   What is a mode shape?

   Hint

   Consider how structures deform when they vibrate.

3. 3.

   What is a natural frequency?

   • Frequency applied externally
   • Frequency at which a system oscillates naturally
   • A forced vibration frequency

   Hint

   Remember, it relates to the system's behavior without outside influence.

4. 4.

   Mode shapes are defined as:

   • True
   • False

   Hint

   Think of how objects deform when they vibrate.

5. 5.

   Given a three-degree-of-freedom system, derive the mass and stiffness matrices, then compute the natural frequencies and mode shapes.

   Hint

   Start with the equations from earlier.

6. 6.

   Analyze a multi-story building structure subjected to seismic load and determine how the mode shapes contribute to the overall response.

   Hint

   Consider how each mode affects the total response.