1. A shaft is 50mm in diameter and 3m long and beam having simply supported boundary condition. The density of the beam 7835, E = 210 GPa. Calculate the first five natural frequencies?

2. How the thickness and width variation influences the natural frequencies?

3. Obtain the natural frequencies of Aluminium and Steel and compare their results?

4. Derive the expression for the nth natural frequency for the following cases?

  • Mixed (fixed-simple) beam
  • Overhang beam
  • Continuous (more than two support)

Simply supported with additional mass m at centre

5. How the natural frequencies vary with the length of the beam?

6. What are the natural frequencies of cantilever beam with end load F?