4.10.2. Importance of Natural Frequency and Mode Shapes

Try these first

1. 1.

   What is natural frequency?

   Hint

   Think about the inherent vibrations of a structure.

2. 2.

   What occurs when a structure's natural frequency matches an external frequency?

   Hint

   Consider what happens to a swing when pushed at the right time.

3. 3.

   What is resonance?

   • A type of amplitude
   • When frequencies match
   • Structural failure

   Hint

   Consider a swing being pushed periodically.

4. 4.

   True or False: Mode shapes are irrelevant to the design of tall buildings.

   • True
   • False

   Hint

   Think about how different building heights affect vibrations.

5. 5.

   A rectangular beam is fixed at both ends. If its dimensions are 4m long, with a width of 0.1m and a height of 0.2m, calculate its first natural frequency knowing the Young's Modulus is 200 GPa.

   Hint

   Refer to relevant beam theory formulas to find your answer.

6. 6.

   A tall building's first natural frequency is found to be 1 Hz. If an earthquake generates a frequency of 1 Hz, explain the potential consequences and solutions engineers could consider.

   Hint

   Think about ways to alter the relationship between the building and the frequency.