14.5.1. Rayleigh’s Method

Try these first

1. 1.

   What does Rayleigh’s Method estimate?

   Hint

   Think about the purpose of the method.

2. 2.

   What happens when the stiffness of a structure increases?

   Hint

   Recall how stiffness affects vibrations.

3. 3.

   What does Rayleigh’s Method primarily calculate?

   • Mass of structures
   • Natural frequencies
   • Load distribution

   Hint

   Focus on the main outcome of the method.

4. 4.

   True or False: Increasing stiffness always leads to lower natural frequencies.

   • True
   • False

   Hint

   Recall the relationship between stiffness and frequency.

5. 5.

   A beam has a stiffness (EI) of 1000 N·m² and a density (ρ) of 7800 kg/m³. Calculate its natural frequency if the cross-sectional area is 0.01 m².

   Hint

   Keep the units consistent while calculating.

6. 6.

   Discuss a situation in which Rayleigh's Method would not provide an accurate estimate of a structure's natural frequency.

   Hint

   Think about the importance of proper assumptions in modeling.