15.1. Free Vibration and Mode Shapes

Try these first

1. 1.

   Define free vibration.

   Hint

   Think about motion after a swing is pushed.

2. 2.

   What corresponds to each mode shape?

   Hint

   How many frequencies are in a multi-degree system?

3. 3.

   What is free vibration?

   • True
   • False

   Hint

   Think about a system left to move after being disturbed.

4. 4.

   Each mode shape in a structure corresponds to:

   • One natural frequency
   • Several natural frequencies
   • No frequencies

   Hint

   How many frequencies match up with each individual deformation shape?

5. 5.

   Analyze a 4-DOF cantilever beam subjected to an initial disturbance and determine the mode shapes and corresponding natural frequencies.

   Hint

   Consider utilizing numerical methods like Rayleigh-Ritz for complex structures.

6. 6.

   In the design of a new building, how would you mitigate the effects of resonance identified from mode shapes? Consider the material properties and structural reinforcement strategies.

   Hint

   Think about how materials can affect vibrations in a structure.