11.15. Rayleigh’s Method for Approximate Frequency

Try these first

1. 1.

   What is the Rayleigh quotient?

   Hint

   Think about how stiffness and mass relate to frequency.

2. 2.

   What is the purpose of a trial shape function in Rayleigh's method?

   Hint

   Consider how we analyze static scenarios.

3. 3.

   What does the Rayleigh quotient help estimate?

   • Static deflection
   • Natural frequency
   • Mass matrix

   Hint

   Focus on the purpose of frequency estimation.

4. 4.

   True or False: The Rayleigh method requires complex numerical calculations.

   • True
   • False

   Hint

   Consider the characteristics of computational solutions.

5. 5.

   A cantilever beam is deflected under its own weight. Use Rayleigh's method to estimate its fundamental frequency with given values for the stiffness and mass.

   Hint

   Remember the equations for a cantilever beam's bending.

6. 6.

   Compare the results obtained from Rayleigh's method with a finite element analysis for the same structure. Discuss the possible discrepancies.

   Hint

   Consider the assumptions made in both methods.